1 files changed, 5 insertions, 1 deletions
diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index 6d13699..6cefb2c 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -77,7 +77,7 @@ class PyJWS:
         self,
         payload: bytes,
         key: str,
-        algorithm: str = "HS256",
+        algorithm: Optional[str] = "HS256",
         headers: Optional[Dict] = None,
         json_encoder: Optional[Type[json.JSONEncoder]] = None,
     ) -> str:
@@ -86,6 +86,10 @@ class PyJWS:
         if algorithm is None:
             algorithm = "none"
 
+        # Prefer headers["alg"] if present to algorithm parameter.
+        if headers and "alg" in headers and headers["alg"]:
+            algorithm = headers["alg"]
+
         if algorithm not in self._valid_algs:
             pass