diff --git a/lib/dispatcher/client-h1.js b/lib/dispatcher/client-h1.js
index 0cb6528ae06..62a3e29ef24 100644
--- a/lib/dispatcher/client-h1.js
+++ b/lib/dispatcher/client-h1.js
@@ -49,7 +49,8 @@ const {
   kMaxResponseSize,
   kListeners,
   kOnError,
-  kResume
+  kResume,
+  kHTTPContext
 } = require('../core/symbols.js')
 
 const constants = require('../llhttp/constants.js')
@@ -403,6 +404,7 @@ class Parser {
     removeAllListeners(socket)
 
     client[kSocket] = null
+    client[kHTTPContext] = null // TODO (fix): This is hacky...
     client[kQueue][client[kRunningIdx]++] = null
     client.emit('disconnect', client[kUrl], [client], new InformationalError('upgrade'))
 
@@ -643,6 +645,8 @@ function onParserTimeout (parser) {
 }
 
 async function connectH1 (client, socket) {
+  client[kSocket] = socket
+
   if (!llhttpInstance) {
     llhttpInstance = await llhttpPromise
     llhttpPromise = null
@@ -706,6 +710,7 @@ async function connectH1 (client, socket) {
     const err = this[kError] || new SocketError('closed', util.getSocketInfo(this))
 
     client[kSocket] = null
+    client[kHTTPContext] = null // TODO (fix): This is hacky...
 
     if (client.destroyed) {
       assert(client[kPending] === 0)
@@ -733,6 +738,11 @@ async function connectH1 (client, socket) {
     client[kResume]()
   })
 
+  let closed = false
+  socket.on('close', () => {
+    closed = true
+  })
+
   return {
     version: 'h1',
     defaultPipelining: 1,
@@ -742,38 +752,48 @@ async function connectH1 (client, socket) {
     resume () {
       resumeH1(client)
     },
-    destroy () {
+    destroy (err, callback) {
+      if (closed) {
+        queueMicrotask(callback)
+      } else {
+        socket.destroy(err).on('close', callback)
+      }
+    },
+    get destroyed () {
+      return socket.destroyed
     },
     busy (request) {
       if (socket[kWriting] || socket[kReset] || socket[kBlocking]) {
         return true
       }
 
-      if (client[kRunning] > 0 && !request.idempotent) {
-        // Non-idempotent request cannot be retried.
-        // Ensure that no other requests are inflight and
-        // could cause failure.
-        return true
-      }
-
-      if (client[kRunning] > 0 && (request.upgrade || request.method === 'CONNECT')) {
-        // Don't dispatch an upgrade until all preceding requests have completed.
-        // A misbehaving server might upgrade the connection before all pipelined
-        // request has completed.
-        return true
-      }
+      if (request) {
+        if (client[kRunning] > 0 && !request.idempotent) {
+          // Non-idempotent request cannot be retried.
+          // Ensure that no other requests are inflight and
+          // could cause failure.
+          return true
+        }
 
-      if (client[kRunning] > 0 && util.bodyLength(request.body) !== 0 &&
-        (util.isStream(request.body) || util.isAsyncIterable(request.body) || util.isFormDataLike(request.body))) {
-        // Request with stream or iterator body can error while other requests
-        // are inflight and indirectly error those as well.
-        // Ensure this doesn't happen by waiting for inflight
-        // to complete before dispatching.
+        if (client[kRunning] > 0 && (request.upgrade || request.method === 'CONNECT')) {
+          // Don't dispatch an upgrade until all preceding requests have completed.
+          // A misbehaving server might upgrade the connection before all pipelined
+          // request has completed.
+          return true
+        }
 
-        // Request with stream or iterator body cannot be retried.
-        // Ensure that no other requests are inflight and
-        // could cause failure.
-        return true
+        if (client[kRunning] > 0 && util.bodyLength(request.body) !== 0 &&
+          (util.isStream(request.body) || util.isAsyncIterable(request.body) || util.isFormDataLike(request.body))) {
+          // Request with stream or iterator body can error while other requests
+          // are inflight and indirectly error those as well.
+          // Ensure this doesn't happen by waiting for inflight
+          // to complete before dispatching.
+
+          // Request with stream or iterator body cannot be retried.
+          // Ensure that no other requests are inflight and
+          // could cause failure.
+          return true
+        }
       }
 
       return false
diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index 7202c654397..1c3791016e7 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -55,6 +55,8 @@ const {
 } = http2
 
 async function connectH2 (client, socket) {
+  client[kSocket] = socket
+
   if (!h2ExperimentalWarned) {
     h2ExperimentalWarned = true
     process.emitWarning('H2 support is experimental, expect them to change at any time.', {
@@ -122,6 +124,11 @@ async function connectH2 (client, socket) {
     util.destroy(this, new SocketError('other side closed', util.getSocketInfo(this)))
   })
 
+  let closed = false
+  socket.on('close', () => {
+    closed = true
+  })
+
   return {
     version: 'h2',
     defaultPipelining: Infinity,
@@ -132,8 +139,16 @@ async function connectH2 (client, socket) {
     resume () {
 
     },
-    destroy (err) {
+    destroy (err, callback) {
       session.destroy(err)
+      if (closed) {
+        queueMicrotask(callback)
+      } else {
+        socket.destroy(err).on('close', callback)
+      }
+    },
+    get destroyed () {
+      return socket.destroyed
     },
     busy () {
       return false
diff --git a/lib/dispatcher/client.js b/lib/dispatcher/client.js
index 7c75c2ff239..8cc334d0baf 100644
--- a/lib/dispatcher/client.js
+++ b/lib/dispatcher/client.js
@@ -17,17 +17,14 @@ const {
 const buildConnector = require('../core/connect.js')
 const {
   kUrl,
-  kReset,
   kServerName,
   kClient,
   kBusy,
   kConnect,
-  kBlocking,
   kResuming,
   kRunning,
   kPending,
   kSize,
-  kWriting,
   kQueue,
   kConnected,
   kConnecting,
@@ -38,7 +35,6 @@ const {
   kRunningIdx,
   kError,
   kPipelining,
-  kSocket,
   kKeepAliveTimeoutValue,
   kMaxHeadersSize,
   kKeepAliveMaxTimeout,
@@ -216,7 +212,6 @@ class Client extends DispatcherBase {
       : [createRedirectInterceptor({ maxRedirections })]
     this[kUrl] = util.parseOrigin(url)
     this[kConnector] = connect
-    this[kSocket] = null
     this[kPipelining] = pipelining != null ? pipelining : 1
     this[kMaxHeadersSize] = maxHeaderSize || http.maxHeaderSize
     this[kKeepAliveDefaultTimeout] = keepAliveTimeout == null ? 4e3 : keepAliveTimeout
@@ -277,13 +272,12 @@ class Client extends DispatcherBase {
   }
 
   get [kConnected] () {
-    return !!this[kSocket] && !this[kConnecting] && !this[kSocket].destroyed
+    return !!this[kHTTPContext] && !this[kConnecting] && !this[kHTTPContext].destroyed
   }
 
   get [kBusy] () {
-    const socket = this[kSocket]
-    return (
-      (socket && (socket[kReset] || socket[kWriting] || socket[kBlocking])) ||
+    return Boolean(
+      this[kHTTPContext]?.busy(null) ||
       (this[kSize] >= (getPipelining(this) || 1)) ||
       this[kPending] > 0
     )
@@ -346,13 +340,9 @@ class Client extends DispatcherBase {
         resolve(null)
       }
 
-      if (this[kHTTPContext] != null) {
-        this[kHTTPContext].destroy(err)
+      if (this[kHTTPContext]) {
+        this[kHTTPContext].destroy(err, callback)
         this[kHTTPContext] = null
-      }
-
-      if (this[kSocket]) {
-        this[kSocket].destroy(err).on('close', callback)
       } else {
         queueMicrotask(callback)
       }
@@ -386,7 +376,7 @@ function onError (client, err) {
 
 async function connect (client) {
   assert(!client[kConnecting])
-  assert(!client[kSocket])
+  assert(!client[kHTTPContext])
 
   let { host, hostname, protocol, port } = client[kUrl]
 
@@ -441,21 +431,24 @@ async function connect (client) {
       return
     }
 
-    client[kConnecting] = false
-
     assert(socket)
 
-    client[kHTTPContext] = socket.alpnProtocol === 'h2'
-      ? await connectH2(client, socket)
-      : await connectH1(client, socket)
+    try {
+      client[kHTTPContext] = socket.alpnProtocol === 'h2'
+        ? await connectH2(client, socket)
+        : await connectH1(client, socket)
+    } catch (err) {
+      socket.destroy().on('error', () => {})
+      throw err
+    }
+
+    client[kConnecting] = false
 
     socket[kCounter] = 0
     socket[kMaxRequests] = client[kMaxRequests]
     socket[kClient] = client
     socket[kError] = null
 
-    client[kSocket] = socket
-
     if (channels.connected.hasSubscribers) {
       channels.connected.publish({
         connectParams: {
@@ -546,8 +539,6 @@ function _resume (client, sync) {
       return
     }
 
-    const socket = client[kSocket]
-
     if (client[kHTTPContext]) {
       client[kHTTPContext].resume()
     }
@@ -580,27 +571,19 @@ function _resume (client, sync) {
       }
 
       client[kServerName] = request.servername
-
-      if (socket && socket.servername !== request.servername) {
-        util.destroy(socket, new InformationalError('servername changed'))
-        return
-      }
+      client[kHTTPContext]?.destroy(new InformationalError('servername changed'))
     }
 
     if (client[kConnecting]) {
       return
     }
 
-    if (!socket) {
+    if (!client[kHTTPContext]) {
       connect(client)
       return
     }
 
-    if (socket.destroyed) {
-      return
-    }
-
-    if (!client[kHTTPContext]) {
+    if (client[kHTTPContext].destroyed) {
       return
     }