diff --git a/internal/converter/components.go b/internal/converter/components.go
index dd00658..4f3f719 100644
--- a/internal/converter/components.go
+++ b/internal/converter/components.go
@@ -36,6 +36,7 @@ func fileToComponents(opts options.Options, fd protoreflect.FileDescriptor) (*hi
 	components.Schemas = stateToSchema(st)
 
 	hasGetRequests := false
+	hasMethods := false
 
 	// Add requestBodies and responses for methods
 	services := fd.Services()
@@ -48,23 +49,10 @@ func fileToComponents(opts options.Options, fd protoreflect.FileDescriptor) (*hi
 			if hasGet {
 				hasGetRequests = true
 			}
+			hasMethods = true
 		}
 	}
 
-	components.Schemas.Set("connect-protocol-version", base.CreateSchemaProxy(&base.Schema{
-		Title:       "Connect-Protocol-Version",
-		Description: "Define the version of the Connect protocol",
-		Type:        []string{"number"},
-		Enum:        []*yaml.Node{utils.CreateIntNode("1")},
-		Const:       utils.CreateIntNode("1"),
-	}))
-
-	components.Schemas.Set("connect-timeout-header", base.CreateSchemaProxy(&base.Schema{
-		Title:       "Connect-Timeout-Ms",
-		Description: "Define the timeout, in ms",
-		Type:        []string{"number"},
-	}))
-
 	if hasGetRequests {
 		components.Schemas.Set("encoding", base.CreateSchemaProxy(&base.Schema{
 			Title:       "encoding",
@@ -91,43 +79,58 @@ func fileToComponents(opts options.Options, fd protoreflect.FileDescriptor) (*hi
 			},
 		}))
 	}
-	connectErrorProps := orderedmap.New[string, *base.SchemaProxy]()
-	connectErrorProps.Set("code", base.CreateSchemaProxy(&base.Schema{
-		Description: "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].",
-		Type:        []string{"string"},
-		Examples:    []*yaml.Node{utils.CreateStringNode("CodeNotFound")},
-		Enum: []*yaml.Node{
-			utils.CreateStringNode("CodeCanceled"),
-			utils.CreateStringNode("CodeUnknown"),
-			utils.CreateStringNode("CodeInvalidArgument"),
-			utils.CreateStringNode("CodeDeadlineExceeded"),
-			utils.CreateStringNode("CodeNotFound"),
-			utils.CreateStringNode("CodeAlreadyExists"),
-			utils.CreateStringNode("CodePermissionDenied"),
-			utils.CreateStringNode("CodeResourceExhausted"),
-			utils.CreateStringNode("CodeFailedPrecondition"),
-			utils.CreateStringNode("CodeAborted"),
-			utils.CreateStringNode("CodeOutOfRange"),
-			utils.CreateStringNode("CodeInternal"),
-			utils.CreateStringNode("CodeUnavailable"),
-			utils.CreateStringNode("CodeDataLoss"),
-			utils.CreateStringNode("CodeUnauthenticated"),
-		},
-	}))
-	connectErrorProps.Set("message", base.CreateSchemaProxy(&base.Schema{
-		Description: "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.",
-		Type:        []string{"string"},
-	}))
-	connectErrorProps.Set("detail", base.CreateSchemaProxyRef("#/components/schemas/google.protobuf.Any"))
-	components.Schemas.Set("connect.error", base.CreateSchemaProxy(&base.Schema{
-		Title:                "Connect Error",
-		Description:          `Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation`,
-		Properties:           connectErrorProps,
-		Type:                 []string{"object"},
-		AdditionalProperties: &base.DynamicValue[*base.SchemaProxy, bool]{N: 1, B: true},
-	}))
-	anyPair := util.NewGoogleAny()
-	components.Schemas.Set(anyPair.ID, base.CreateSchemaProxy(anyPair.Schema))
+	if hasMethods {
+		components.Schemas.Set("connect-protocol-version", base.CreateSchemaProxy(&base.Schema{
+			Title:       "Connect-Protocol-Version",
+			Description: "Define the version of the Connect protocol",
+			Type:        []string{"number"},
+			Enum:        []*yaml.Node{utils.CreateIntNode("1")},
+			Const:       utils.CreateIntNode("1"),
+		}))
+
+		components.Schemas.Set("connect-timeout-header", base.CreateSchemaProxy(&base.Schema{
+			Title:       "Connect-Timeout-Ms",
+			Description: "Define the timeout, in ms",
+			Type:        []string{"number"},
+		}))
+		connectErrorProps := orderedmap.New[string, *base.SchemaProxy]()
+		connectErrorProps.Set("code", base.CreateSchemaProxy(&base.Schema{
+			Description: "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].",
+			Type:        []string{"string"},
+			Examples:    []*yaml.Node{utils.CreateStringNode("CodeNotFound")},
+			Enum: []*yaml.Node{
+				utils.CreateStringNode("CodeCanceled"),
+				utils.CreateStringNode("CodeUnknown"),
+				utils.CreateStringNode("CodeInvalidArgument"),
+				utils.CreateStringNode("CodeDeadlineExceeded"),
+				utils.CreateStringNode("CodeNotFound"),
+				utils.CreateStringNode("CodeAlreadyExists"),
+				utils.CreateStringNode("CodePermissionDenied"),
+				utils.CreateStringNode("CodeResourceExhausted"),
+				utils.CreateStringNode("CodeFailedPrecondition"),
+				utils.CreateStringNode("CodeAborted"),
+				utils.CreateStringNode("CodeOutOfRange"),
+				utils.CreateStringNode("CodeInternal"),
+				utils.CreateStringNode("CodeUnavailable"),
+				utils.CreateStringNode("CodeDataLoss"),
+				utils.CreateStringNode("CodeUnauthenticated"),
+			},
+		}))
+		connectErrorProps.Set("message", base.CreateSchemaProxy(&base.Schema{
+			Description: "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.",
+			Type:        []string{"string"},
+		}))
+		connectErrorProps.Set("detail", base.CreateSchemaProxyRef("#/components/schemas/google.protobuf.Any"))
+		components.Schemas.Set("connect.error", base.CreateSchemaProxy(&base.Schema{
+			Title:                "Connect Error",
+			Description:          `Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation`,
+			Properties:           connectErrorProps,
+			Type:                 []string{"object"},
+			AdditionalProperties: &base.DynamicValue[*base.SchemaProxy, bool]{N: 1, B: true},
+		}))
+		anyPair := util.NewGoogleAny()
+		components.Schemas.Set(anyPair.ID, base.CreateSchemaProxy(anyPair.Schema))
+	}
 
 	return components, nil
 }
diff --git a/internal/converter/converter.go b/internal/converter/converter.go
index 4ab3495..ebd7fd9 100644
--- a/internal/converter/converter.go
+++ b/internal/converter/converter.go
@@ -181,11 +181,6 @@ func ConvertWithOptions(req *pluginpb.CodeGeneratorRequest, opts options.Options
 }
 
 func specToFile(opts options.Options, spec *v3.Document) (string, error) {
-	if opts.TrimUnusedTypes {
-		if err := trimUnusedTypes(spec); err != nil {
-			return "", err
-		}
-	}
 	switch opts.Format {
 	case "yaml":
 		return string(spec.RenderWithIndention(2)), nil
@@ -200,32 +195,6 @@ func specToFile(opts options.Options, spec *v3.Document) (string, error) {
 	}
 }
 
-func trimUnusedTypes(spec *v3.Document) error {
-	slog.Debug("trimming unused types")
-	b, err := spec.Render()
-	if err != nil {
-		return err
-	}
-	doc, err := libopenapi.NewDocument(b)
-	if err != nil {
-		return err
-	}
-	model, errs := doc.BuildV3Model()
-	if errs != nil {
-		return errors.Join(errs...)
-	}
-	model.Index.BuildIndex()
-	references := model.Model.Rolodex.GetRootIndex().GetAllReferences()
-	for pair := spec.Components.Schemas.First(); pair != nil; pair = pair.Next() {
-		ref := fmt.Sprintf("#/components/schemas/%s", pair.Key())
-		if _, ok := references[ref]; !ok {
-			slog.Debug("trimming unused type", "name", pair.Key())
-			spec.Components.Schemas.Delete(pair.Key())
-		}
-	}
-	return nil
-}
-
 func appendToSpec(opts options.Options, spec *v3.Document, fd protoreflect.FileDescriptor) error {
 	gnostic.SpecWithFileAnnotations(spec, fd)
 	components, err := fileToComponents(opts, fd)
diff --git a/internal/converter/schema.go b/internal/converter/schema.go
index d6d443a..5a33756 100644
--- a/internal/converter/schema.go
+++ b/internal/converter/schema.go
@@ -34,16 +34,19 @@ func NewState(opts options.Options) *State {
 func (st *State) CollectFile(tt protoreflect.FileDescriptor) {
 	st.CurrentFile = tt
 
-	// Files can have enums
-	enums := tt.Enums()
-	for i := 0; i < enums.Len(); i++ {
-		st.CollectEnum(enums.Get(i))
-	}
+	// Only collect types from the root if TrimUnusedTypes is off
+	if !st.Opts.TrimUnusedTypes {
+		// Files can have enums
+		enums := tt.Enums()
+		for i := 0; i < enums.Len(); i++ {
+			st.CollectEnum(enums.Get(i))
+		}
 
-	// Files can have messages
-	messages := tt.Messages()
-	for i := 0; i < messages.Len(); i++ {
-		st.CollectMessage(messages.Get(i))
+		// Files can have messages
+		messages := tt.Messages()
+		for i := 0; i < messages.Len(); i++ {
+			st.CollectMessage(messages.Get(i))
+		}
 	}
 
 	// Also make sure to pick up messages referenced in service methods
diff --git a/internal/converter/testdata/fileset.binpb b/internal/converter/testdata/fileset.binpb
index a85806d..245996e 100644
Binary files a/internal/converter/testdata/fileset.binpb and b/internal/converter/testdata/fileset.binpb differ
diff --git a/internal/converter/testdata/proto_names/output/proto_names.openapi.json b/internal/converter/testdata/proto_names/output/proto_names.openapi.json
index bc1eeb9..1959084 100644
--- a/internal/converter/testdata/proto_names/output/proto_names.openapi.json
+++ b/internal/converter/testdata/proto_names/output/proto_names.openapi.json
@@ -32,77 +32,6 @@
         },
         "title": "Message",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/proto_names/output/proto_names.openapi.yaml b/internal/converter/testdata/proto_names/output/proto_names.openapi.yaml
index 135c555..be73749 100644
--- a/internal/converter/testdata/proto_names/output/proto_names.openapi.yaml
+++ b/internal/converter/testdata/proto_names/output/proto_names.openapi.yaml
@@ -24,60 +24,4 @@ components:
           title: UPPER_SNAKE_CASE
       title: Message
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/array_of_enums.openapi.json b/internal/converter/testdata/standard/output/array_of_enums.openapi.json
index 89dee80..eac9fd9 100644
--- a/internal/converter/testdata/standard/output/array_of_enums.openapi.json
+++ b/internal/converter/testdata/standard/output/array_of_enums.openapi.json
@@ -31,77 +31,6 @@
         },
         "title": "ArrayOfEnums",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/array_of_enums.openapi.yaml b/internal/converter/testdata/standard/output/array_of_enums.openapi.yaml
index f781a29..8a6387f 100644
--- a/internal/converter/testdata/standard/output/array_of_enums.openapi.yaml
+++ b/internal/converter/testdata/standard/output/array_of_enums.openapi.yaml
@@ -23,60 +23,4 @@ components:
           title: stuff
       title: ArrayOfEnums
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/array_of_messages.openapi.json b/internal/converter/testdata/standard/output/array_of_messages.openapi.json
index c9a64f0..8e47a9c 100644
--- a/internal/converter/testdata/standard/output/array_of_messages.openapi.json
+++ b/internal/converter/testdata/standard/output/array_of_messages.openapi.json
@@ -34,77 +34,6 @@
         },
         "title": "Thing",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/array_of_messages.openapi.yaml b/internal/converter/testdata/standard/output/array_of_messages.openapi.yaml
index 2e8c1bb..7ddc7e2 100644
--- a/internal/converter/testdata/standard/output/array_of_messages.openapi.yaml
+++ b/internal/converter/testdata/standard/output/array_of_messages.openapi.yaml
@@ -25,60 +25,4 @@ components:
           title: name
       title: Thing
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/editions_2023.openapi.json b/internal/converter/testdata/standard/output/editions_2023.openapi.json
index 18bdd50..45e1620 100644
--- a/internal/converter/testdata/standard/output/editions_2023.openapi.json
+++ b/internal/converter/testdata/standard/output/editions_2023.openapi.json
@@ -49,77 +49,6 @@
         },
         "title": "Person",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/editions_2023.openapi.yaml b/internal/converter/testdata/standard/output/editions_2023.openapi.yaml
index ce47f2c..e5a0d6e 100644
--- a/internal/converter/testdata/standard/output/editions_2023.openapi.yaml
+++ b/internal/converter/testdata/standard/output/editions_2023.openapi.yaml
@@ -34,60 +34,4 @@ components:
             - $ref: '#/components/schemas/editions.Person.Employment'
       title: Person
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/gnostic.openapi.json b/internal/converter/testdata/standard/output/gnostic.openapi.json
index 85f1add..8003fa8 100644
--- a/internal/converter/testdata/standard/output/gnostic.openapi.json
+++ b/internal/converter/testdata/standard/output/gnostic.openapi.json
@@ -237,20 +237,6 @@
         "additionalProperties": false,
         "description": "Custom description for a message"
       },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
       "encoding": {
         "title": "encoding",
         "enum": [
@@ -273,6 +259,20 @@
         ],
         "description": "Which compression algorithm to use for this request"
       },
+      "connect-protocol-version": {
+        "type": "number",
+        "title": "Connect-Protocol-Version",
+        "enum": [
+          1
+        ],
+        "description": "Define the version of the Connect protocol",
+        "const": 1
+      },
+      "connect-timeout-header": {
+        "type": "number",
+        "title": "Connect-Timeout-Ms",
+        "description": "Define the timeout, in ms"
+      },
       "connect.error": {
         "type": "object",
         "properties": {
diff --git a/internal/converter/testdata/standard/output/gnostic.openapi.yaml b/internal/converter/testdata/standard/output/gnostic.openapi.yaml
index e073392..317eff2 100644
--- a/internal/converter/testdata/standard/output/gnostic.openapi.yaml
+++ b/internal/converter/testdata/standard/output/gnostic.openapi.yaml
@@ -151,17 +151,6 @@ components:
       title: Custom title for a message
       additionalProperties: false
       description: Custom description for a message
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
     encoding:
       title: encoding
       enum:
@@ -179,6 +168,17 @@ components:
         - gzip
         - br
       description: Which compression algorithm to use for this request
+    connect-protocol-version:
+      type: number
+      title: Connect-Protocol-Version
+      enum:
+        - 1
+      description: Define the version of the Connect protocol
+      const: 1
+    connect-timeout-header:
+      type: number
+      title: Connect-Timeout-Ms
+      description: Define the timeout, in ms
     connect.error:
       type: object
       properties:
diff --git a/internal/converter/testdata/standard/output/googleapi.openapi.json b/internal/converter/testdata/standard/output/googleapi.openapi.json
index 438251a..8daee1c 100644
--- a/internal/converter/testdata/standard/output/googleapi.openapi.json
+++ b/internal/converter/testdata/standard/output/googleapi.openapi.json
@@ -42,20 +42,6 @@
         "type": "object",
         "description": "A generic empty message that you can re-use to avoid defining duplicated\n empty messages in your APIs. A typical example is to use it as the request\n or the response type of an API method. For instance:\n\n     service Foo {\n       rpc Bar(google.protobuf.Empty) returns (google.protobuf.Empty);\n     }"
       },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
       "encoding": {
         "title": "encoding",
         "enum": [
@@ -78,6 +64,20 @@
         ],
         "description": "Which compression algorithm to use for this request"
       },
+      "connect-protocol-version": {
+        "type": "number",
+        "title": "Connect-Protocol-Version",
+        "enum": [
+          1
+        ],
+        "description": "Define the version of the Connect protocol",
+        "const": 1
+      },
+      "connect-timeout-header": {
+        "type": "number",
+        "title": "Connect-Timeout-Ms",
+        "description": "Define the timeout, in ms"
+      },
       "connect.error": {
         "type": "object",
         "properties": {
diff --git a/internal/converter/testdata/standard/output/googleapi.openapi.yaml b/internal/converter/testdata/standard/output/googleapi.openapi.yaml
index dfb659c..9f0cc2e 100644
--- a/internal/converter/testdata/standard/output/googleapi.openapi.yaml
+++ b/internal/converter/testdata/standard/output/googleapi.openapi.yaml
@@ -33,17 +33,6 @@ components:
              service Foo {
                rpc Bar(google.protobuf.Empty) returns (google.protobuf.Empty);
              }
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
     encoding:
       title: encoding
       enum:
@@ -61,6 +50,17 @@ components:
         - gzip
         - br
       description: Which compression algorithm to use for this request
+    connect-protocol-version:
+      type: number
+      title: Connect-Protocol-Version
+      enum:
+        - 1
+      description: Define the version of the Connect protocol
+      const: 1
+    connect-timeout-header:
+      type: number
+      title: Connect-Timeout-Ms
+      description: Define the timeout, in ms
     connect.error:
       type: object
       properties:
diff --git a/internal/converter/testdata/standard/output/helloworld.openapi.json b/internal/converter/testdata/standard/output/helloworld.openapi.json
index 6eb0ca5..0551aad 100644
--- a/internal/converter/testdata/standard/output/helloworld.openapi.json
+++ b/internal/converter/testdata/standard/output/helloworld.openapi.json
@@ -251,20 +251,6 @@
         "additionalProperties": false,
         "description": "The request message containing the user's name."
       },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
       "encoding": {
         "title": "encoding",
         "enum": [
@@ -287,6 +273,20 @@
         ],
         "description": "Which compression algorithm to use for this request"
       },
+      "connect-protocol-version": {
+        "type": "number",
+        "title": "Connect-Protocol-Version",
+        "enum": [
+          1
+        ],
+        "description": "Define the version of the Connect protocol",
+        "const": 1
+      },
+      "connect-timeout-header": {
+        "type": "number",
+        "title": "Connect-Timeout-Ms",
+        "description": "Define the timeout, in ms"
+      },
       "connect.error": {
         "type": "object",
         "properties": {
diff --git a/internal/converter/testdata/standard/output/helloworld.openapi.yaml b/internal/converter/testdata/standard/output/helloworld.openapi.yaml
index 0ca8bd8..c1ef506 100644
--- a/internal/converter/testdata/standard/output/helloworld.openapi.yaml
+++ b/internal/converter/testdata/standard/output/helloworld.openapi.yaml
@@ -153,17 +153,6 @@ components:
       title: HelloRequest
       additionalProperties: false
       description: The request message containing the user's name.
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
     encoding:
       title: encoding
       enum:
@@ -181,6 +170,17 @@ components:
         - gzip
         - br
       description: Which compression algorithm to use for this request
+    connect-protocol-version:
+      type: number
+      title: Connect-Protocol-Version
+      enum:
+        - 1
+      description: Define the version of the Connect protocol
+      const: 1
+    connect-timeout-header:
+      type: number
+      title: Connect-Timeout-Ms
+      description: Define the timeout, in ms
     connect.error:
       type: object
       properties:
diff --git a/internal/converter/testdata/standard/output/json_name.openapi.json b/internal/converter/testdata/standard/output/json_name.openapi.json
index d75d753..33d5f44 100644
--- a/internal/converter/testdata/standard/output/json_name.openapi.json
+++ b/internal/converter/testdata/standard/output/json_name.openapi.json
@@ -31,77 +31,6 @@
         },
         "title": "Message",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/json_name.openapi.yaml b/internal/converter/testdata/standard/output/json_name.openapi.yaml
index 03906af..834c008 100644
--- a/internal/converter/testdata/standard/output/json_name.openapi.yaml
+++ b/internal/converter/testdata/standard/output/json_name.openapi.yaml
@@ -23,60 +23,4 @@ components:
           title: stuff
       title: Message
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/petstore.openapi.json b/internal/converter/testdata/standard/output/petstore.openapi.json
index fa9e3b0..9b90fa3 100644
--- a/internal/converter/testdata/standard/output/petstore.openapi.json
+++ b/internal/converter/testdata/standard/output/petstore.openapi.json
@@ -707,20 +707,6 @@
         "title": "UploadFileReq",
         "additionalProperties": false
       },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
       "encoding": {
         "title": "encoding",
         "enum": [
@@ -743,6 +729,20 @@
         ],
         "description": "Which compression algorithm to use for this request"
       },
+      "connect-protocol-version": {
+        "type": "number",
+        "title": "Connect-Protocol-Version",
+        "enum": [
+          1
+        ],
+        "description": "Define the version of the Connect protocol",
+        "const": 1
+      },
+      "connect-timeout-header": {
+        "type": "number",
+        "title": "Connect-Timeout-Ms",
+        "description": "Define the timeout, in ms"
+      },
       "connect.error": {
         "type": "object",
         "properties": {
diff --git a/internal/converter/testdata/standard/output/petstore.openapi.yaml b/internal/converter/testdata/standard/output/petstore.openapi.yaml
index 17fc06a..bc733a6 100644
--- a/internal/converter/testdata/standard/output/petstore.openapi.yaml
+++ b/internal/converter/testdata/standard/output/petstore.openapi.yaml
@@ -458,17 +458,6 @@ components:
           title: file
       title: UploadFileReq
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
     encoding:
       title: encoding
       enum:
@@ -486,6 +475,17 @@ components:
         - gzip
         - br
       description: Which compression algorithm to use for this request
+    connect-protocol-version:
+      type: number
+      title: Connect-Protocol-Version
+      enum:
+        - 1
+      description: Define the version of the Connect protocol
+      const: 1
+    connect-timeout-header:
+      type: number
+      title: Connect-Timeout-Ms
+      description: Define the timeout, in ms
     connect.error:
       type: object
       properties:
diff --git a/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.json b/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.json
index eef9f27..9d4d6ae 100644
--- a/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.json
@@ -109,20 +109,6 @@
         ],
         "additionalProperties": false
       },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
       "encoding": {
         "title": "encoding",
         "enum": [
@@ -145,6 +131,20 @@
         ],
         "description": "Which compression algorithm to use for this request"
       },
+      "connect-protocol-version": {
+        "type": "number",
+        "title": "Connect-Protocol-Version",
+        "enum": [
+          1
+        ],
+        "description": "Define the version of the Connect protocol",
+        "const": 1
+      },
+      "connect-timeout-header": {
+        "type": "number",
+        "title": "Connect-Timeout-Ms",
+        "description": "Define the timeout, in ms"
+      },
       "connect.error": {
         "type": "object",
         "properties": {
diff --git a/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.yaml
index b5ce71f..fe3f57a 100644
--- a/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate-and-googleapi.openapi.yaml
@@ -63,17 +63,6 @@ components:
       required:
         - name
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
     encoding:
       title: encoding
       enum:
@@ -91,6 +80,17 @@ components:
         - gzip
         - br
       description: Which compression algorithm to use for this request
+    connect-protocol-version:
+      type: number
+      title: Connect-Protocol-Version
+      enum:
+        - 1
+      description: Define the version of the Connect protocol
+      const: 1
+    connect-timeout-header:
+      type: number
+      title: Connect-Timeout-Ms
+      description: Define the timeout, in ms
     connect.error:
       type: object
       properties:
diff --git a/internal/converter/testdata/standard/output/protovalidate.custom.openapi.json b/internal/converter/testdata/standard/output/protovalidate.custom.openapi.json
index 5fb161a..ccb7e49 100644
--- a/internal/converter/testdata/standard/output/protovalidate.custom.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate.custom.openapi.json
@@ -18,77 +18,6 @@
         },
         "title": "User",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/protovalidate.custom.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate.custom.openapi.yaml
index 1c26a8a..88f27c4 100644
--- a/internal/converter/testdata/standard/output/protovalidate.custom.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate.custom.openapi.yaml
@@ -19,60 +19,4 @@ components:
 
       title: User
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/protovalidate.fields.openapi.json b/internal/converter/testdata/standard/output/protovalidate.fields.openapi.json
index 57d0938..6e823a9 100644
--- a/internal/converter/testdata/standard/output/protovalidate.fields.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate.fields.openapi.json
@@ -16,77 +16,6 @@
         },
         "title": "User",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/protovalidate.fields.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate.fields.openapi.yaml
index e8d26e0..2b76678 100644
--- a/internal/converter/testdata/standard/output/protovalidate.fields.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate.fields.openapi.yaml
@@ -13,60 +13,4 @@ components:
           format: int32
       title: User
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/protovalidate.message.openapi.json b/internal/converter/testdata/standard/output/protovalidate.message.openapi.json
index 503269f..085a106 100644
--- a/internal/converter/testdata/standard/output/protovalidate.message.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate.message.openapi.json
@@ -37,77 +37,6 @@
         "title": "Allocation",
         "additionalProperties": false,
         "description": "Used should be less or equal to the total size:\n```\nthis.used \u003c= this.total_size\n```\n\n"
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/protovalidate.message.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate.message.openapi.yaml
index 2c334ae..26ff1e4 100644
--- a/internal/converter/testdata/standard/output/protovalidate.message.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate.message.openapi.yaml
@@ -28,60 +28,4 @@ components:
         this.used <= this.total_size
         ```
 
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.json b/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.json
index ebfedd9..d733399 100644
--- a/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.json
@@ -3398,77 +3398,6 @@
         },
         "title": "UInt64NotIn",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.yaml
index 1606a0d..d48aa0d 100644
--- a/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate.numbers.openapi.yaml
@@ -2313,60 +2313,4 @@ components:
           title: val
       title: UInt64NotIn
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/protovalidate.strings.openapi.json b/internal/converter/testdata/standard/output/protovalidate.strings.openapi.json
index 3f21c91..d880c61 100644
--- a/internal/converter/testdata/standard/output/protovalidate.strings.openapi.json
+++ b/internal/converter/testdata/standard/output/protovalidate.strings.openapi.json
@@ -756,77 +756,6 @@
         },
         "title": "StringUUIDIgnore",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/protovalidate.strings.openapi.yaml b/internal/converter/testdata/standard/output/protovalidate.strings.openapi.yaml
index fe4b47c..228564d 100644
--- a/internal/converter/testdata/standard/output/protovalidate.strings.openapi.yaml
+++ b/internal/converter/testdata/standard/output/protovalidate.strings.openapi.yaml
@@ -547,60 +547,4 @@ components:
           format: uuid
       title: StringUUIDIgnore
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/standard/output/test.openapi.json b/internal/converter/testdata/standard/output/test.openapi.json
index cbab4ef..8637cc9 100644
--- a/internal/converter/testdata/standard/output/test.openapi.json
+++ b/internal/converter/testdata/standard/output/test.openapi.json
@@ -2784,77 +2784,6 @@
         },
         "title": "StringValueMapEntry",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/standard/output/test.openapi.yaml b/internal/converter/testdata/standard/output/test.openapi.yaml
index a6bc635..f8ba0be 100644
--- a/internal/converter/testdata/standard/output/test.openapi.yaml
+++ b/internal/converter/testdata/standard/output/test.openapi.yaml
@@ -1994,60 +1994,4 @@ components:
             - $ref: '#/components/schemas/google.protobuf.StringValue'
       title: StringValueMapEntry
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []
diff --git a/internal/converter/testdata/trim_unused_type/has_unused.proto b/internal/converter/testdata/trim_unused_type/has_unused.proto
index 87959db..6720152 100644
--- a/internal/converter/testdata/trim_unused_type/has_unused.proto
+++ b/internal/converter/testdata/trim_unused_type/has_unused.proto
@@ -25,4 +25,19 @@ message UsedType {
 
 message Unused {
   string unused_field = 1;
+  UnusedChild unused_child = 2;
+  UnusedChild2 unused_child2 = 3;
+}
+
+message UnusedChild {
+  string unused_child_field = 1;
+  UnusedChild3 unused_child3 = 2;
+}
+
+message UnusedChild2 {
+  string unused_child_field = 1;
+}
+
+message UnusedChild3 {
+  string unused_child_field = 1;
 }
diff --git a/internal/converter/testdata/with_base/output/empty.openapi.json b/internal/converter/testdata/with_base/output/empty.openapi.json
index 101f7d3..bfe500c 100644
--- a/internal/converter/testdata/with_base/output/empty.openapi.json
+++ b/internal/converter/testdata/with_base/output/empty.openapi.json
@@ -11,70 +11,6 @@
         "scheme": "bearer",
         "bearerFormat": "JWT"
       }
-    },
-    "schemas": {
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
-      }
     }
   },
   "security": [
diff --git a/internal/converter/testdata/with_base/output/empty.openapi.yaml b/internal/converter/testdata/with_base/output/empty.openapi.yaml
index da94b35..60cab00 100644
--- a/internal/converter/testdata/with_base/output/empty.openapi.yaml
+++ b/internal/converter/testdata/with_base/output/empty.openapi.yaml
@@ -8,56 +8,6 @@ components:
       type: http
       scheme: bearer
       bearerFormat: JWT
-  schemas:
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security:
   - bearerAuth: []
 paths: {}
diff --git a/internal/converter/testdata/with_proto_annotations/output/test.openapi.json b/internal/converter/testdata/with_proto_annotations/output/test.openapi.json
index 268ec32..831499b 100644
--- a/internal/converter/testdata/with_proto_annotations/output/test.openapi.json
+++ b/internal/converter/testdata/with_proto_annotations/output/test.openapi.json
@@ -3020,77 +3020,6 @@
         },
         "title": "StringValueMapEntry",
         "additionalProperties": false
-      },
-      "connect-protocol-version": {
-        "type": "number",
-        "title": "Connect-Protocol-Version",
-        "enum": [
-          1
-        ],
-        "description": "Define the version of the Connect protocol",
-        "const": 1
-      },
-      "connect-timeout-header": {
-        "type": "number",
-        "title": "Connect-Timeout-Ms",
-        "description": "Define the timeout, in ms"
-      },
-      "connect.error": {
-        "type": "object",
-        "properties": {
-          "code": {
-            "type": "string",
-            "examples": [
-              "CodeNotFound"
-            ],
-            "enum": [
-              "CodeCanceled",
-              "CodeUnknown",
-              "CodeInvalidArgument",
-              "CodeDeadlineExceeded",
-              "CodeNotFound",
-              "CodeAlreadyExists",
-              "CodePermissionDenied",
-              "CodeResourceExhausted",
-              "CodeFailedPrecondition",
-              "CodeAborted",
-              "CodeOutOfRange",
-              "CodeInternal",
-              "CodeUnavailable",
-              "CodeDataLoss",
-              "CodeUnauthenticated"
-            ],
-            "description": "The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code]."
-          },
-          "message": {
-            "type": "string",
-            "description": "A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client."
-          },
-          "detail": {
-            "$ref": "#/components/schemas/google.protobuf.Any"
-          }
-        },
-        "title": "Connect Error",
-        "additionalProperties": true,
-        "description": "Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation"
-      },
-      "google.protobuf.Any": {
-        "type": "object",
-        "properties": {
-          "type": {
-            "type": "string"
-          },
-          "value": {
-            "type": "string",
-            "format": "binary"
-          },
-          "debug": {
-            "type": "object",
-            "additionalProperties": true
-          }
-        },
-        "additionalProperties": true,
-        "description": "Contains an arbitrary serialized message along with a @type that describes the type of the serialized message."
       }
     }
   },
diff --git a/internal/converter/testdata/with_proto_annotations/output/test.openapi.yaml b/internal/converter/testdata/with_proto_annotations/output/test.openapi.yaml
index 8e3065d..8753c89 100644
--- a/internal/converter/testdata/with_proto_annotations/output/test.openapi.yaml
+++ b/internal/converter/testdata/with_proto_annotations/output/test.openapi.yaml
@@ -2230,60 +2230,4 @@ components:
             - $ref: '#/components/schemas/google.protobuf.StringValue'
       title: StringValueMapEntry
       additionalProperties: false
-    connect-protocol-version:
-      type: number
-      title: Connect-Protocol-Version
-      enum:
-        - 1
-      description: Define the version of the Connect protocol
-      const: 1
-    connect-timeout-header:
-      type: number
-      title: Connect-Timeout-Ms
-      description: Define the timeout, in ms
-    connect.error:
-      type: object
-      properties:
-        code:
-          type: string
-          examples:
-            - CodeNotFound
-          enum:
-            - CodeCanceled
-            - CodeUnknown
-            - CodeInvalidArgument
-            - CodeDeadlineExceeded
-            - CodeNotFound
-            - CodeAlreadyExists
-            - CodePermissionDenied
-            - CodeResourceExhausted
-            - CodeFailedPrecondition
-            - CodeAborted
-            - CodeOutOfRange
-            - CodeInternal
-            - CodeUnavailable
-            - CodeDataLoss
-            - CodeUnauthenticated
-          description: The status code, which should be an enum value of [google.rpc.Code][google.rpc.Code].
-        message:
-          type: string
-          description: A developer-facing error message, which should be in English. Any user-facing error message should be localized and sent in the [google.rpc.Status.details][google.rpc.Status.details] field, or localized by the client.
-        detail:
-          $ref: '#/components/schemas/google.protobuf.Any'
-      title: Connect Error
-      additionalProperties: true
-      description: 'Error type returned by Connect: https://connectrpc.com/docs/go/errors/#http-representation'
-    google.protobuf.Any:
-      type: object
-      properties:
-        type:
-          type: string
-        value:
-          type: string
-          format: binary
-        debug:
-          type: object
-          additionalProperties: true
-      additionalProperties: true
-      description: Contains an arbitrary serialized message along with a @type that describes the type of the serialized message.
 security: []