diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index ab8490f9..c914db19 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -101,6 +101,7 @@ def encode(
         headers: dict[str, Any] | None = None,
         json_encoder: Type[json.JSONEncoder] | None = None,
         is_payload_detached: bool = False,
+        sort_headers: bool = True,
     ) -> str:
         segments = []
 
@@ -133,9 +134,8 @@ def encode(
             # True is the standard value for b64, so no need for it
             del header["b64"]
 
-        # Fix for headers misorder - issue #715
         json_header = json.dumps(
-            header, separators=(",", ":"), cls=json_encoder, sort_keys=True
+            header, separators=(",", ":"), cls=json_encoder, sort_keys=sort_headers
         ).encode()
 
         segments.append(base64url_encode(json_header))
diff --git a/jwt/api_jwt.py b/jwt/api_jwt.py
index e1df3c7b..5d21afc3 100644
--- a/jwt/api_jwt.py
+++ b/jwt/api_jwt.py
@@ -45,6 +45,7 @@ def encode(
         algorithm: Optional[str] = "HS256",
         headers: Optional[Dict[str, Any]] = None,
         json_encoder: Optional[Type[json.JSONEncoder]] = None,
+        sort_headers: bool = True,
     ) -> str:
         # Check that we get a mapping
         if not isinstance(payload, Mapping):
@@ -66,7 +67,14 @@ def encode(
             json_encoder=json_encoder,
         )
 
-        return api_jws.encode(json_payload, key, algorithm, headers, json_encoder)
+        return api_jws.encode(
+            json_payload,
+            key,
+            algorithm,
+            headers,
+            json_encoder,
+            sort_headers=sort_headers,
+        )
 
     def _encode_payload(
         self,
diff --git a/tests/test_api_jws.py b/tests/test_api_jws.py
index cfbbe212..fe6c2d4f 100644
--- a/tests/test_api_jws.py
+++ b/tests/test_api_jws.py
@@ -414,6 +414,17 @@ def test_bytes_secret(self, jws, payload):
 
         assert decoded_payload == payload
 
+    @pytest.mark.parametrize("sort_headers", (False, True))
+    def test_sorting_of_headers(self, jws, payload, sort_headers):
+        jws_message = jws.encode(
+            payload,
+            key="\xc2",
+            headers={"b": "1", "a": "2"},
+            sort_headers=sort_headers,
+        )
+        header_json = base64url_decode(jws_message.split(".")[0])
+        assert sort_headers == (header_json.index(b'"a"') < header_json.index(b'"b"'))
+
     def test_decode_invalid_header_padding(self, jws):
         example_jws = (
             "aeyJhbGciOiAiSFMyNTYiLCAidHlwIjogIkpXVCJ9"