diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 763822a1..b049e9e8 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -13,6 +13,7 @@ Changed
 Fixed
 ~~~~~
 
+- Prefer `headers["alg"]` to `algorithm` in `jwt.encode()`. `#673 <https://github.com/jpadilla/pyjwt/pull/673>`__
 - Fix aud validation to support {'aud': null} case. `#670 <https://github.com/jpadilla/pyjwt/pull/670>`__
 
 Added
diff --git a/docs/api.rst b/docs/api.rst
index d23d4bdd..f1720b93 100644
--- a/docs/api.rst
+++ b/docs/api.rst
@@ -13,8 +13,9 @@ API Reference
         * for **asymmetric algorithms**: PEM-formatted private key, a multiline string
         * for **symmetric algorithms**: plain string, sufficiently long for security
 
-    :param str algorithm: algorithm to sign the token with, e.g. ``"ES256"``
-    :param dict headers: additional JWT header fields, e.g. ``dict(kid="my-key-id")``
+    :param str algorithm: algorithm to sign the token with, e.g. ``"ES256"``.
+        If ``headers`` includes ``alg``, it will be preferred to this parameter.
+    :param dict headers: additional JWT header fields, e.g. ``dict(kid="my-key-id")``.
     :param json.JSONEncoder json_encoder: custom JSON encoder for ``payload`` and ``headers``
     :rtype: str
     :returns: a JSON Web Token
diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index 6d136999..6cefb2c2 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -77,7 +77,7 @@ def encode(
         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 @@ def encode(
         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
 
diff --git a/jwt/api_jwt.py b/jwt/api_jwt.py
index 55a8f291..48a93162 100644
--- a/jwt/api_jwt.py
+++ b/jwt/api_jwt.py
@@ -38,7 +38,7 @@ def encode(
         self,
         payload: Dict[str, Any],
         key: str,
-        algorithm: str = "HS256",
+        algorithm: Optional[str] = "HS256",
         headers: Optional[Dict] = None,
         json_encoder: Optional[Type[json.JSONEncoder]] = None,
     ) -> str:
diff --git a/tests/test_api_jws.py b/tests/test_api_jws.py
index b731edce..fbeda024 100644
--- a/tests/test_api_jws.py
+++ b/tests/test_api_jws.py
@@ -166,6 +166,32 @@ def test_encode_algorithm_param_should_be_case_sensitive(self, jws, payload):
         exception = context.value
         assert str(exception) == "Algorithm not supported"
 
+    def test_encode_with_headers_alg_none(self, jws, payload):
+        msg = jws.encode(payload, key=None, headers={"alg": "none"})
+        with pytest.raises(DecodeError) as context:
+            jws.decode(msg, algorithms=["none"])
+        assert str(context.value) == "Signature verification failed"
+
+    @crypto_required
+    def test_encode_with_headers_alg_es256(self, jws, payload):
+        with open(key_path("testkey_ec.priv"), "rb") as ec_priv_file:
+            priv_key = load_pem_private_key(ec_priv_file.read(), password=None)
+        with open(key_path("testkey_ec.pub"), "rb") as ec_pub_file:
+            pub_key = load_pem_public_key(ec_pub_file.read())
+
+        msg = jws.encode(payload, priv_key, headers={"alg": "ES256"})
+        assert b"hello world" == jws.decode(msg, pub_key, algorithms=["ES256"])
+
+    @crypto_required
+    def test_encode_with_alg_hs256_and_headers_alg_es256(self, jws, payload):
+        with open(key_path("testkey_ec.priv"), "rb") as ec_priv_file:
+            priv_key = load_pem_private_key(ec_priv_file.read(), password=None)
+        with open(key_path("testkey_ec.pub"), "rb") as ec_pub_file:
+            pub_key = load_pem_public_key(ec_pub_file.read())
+
+        msg = jws.encode(payload, priv_key, algorithm="HS256", headers={"alg": "ES256"})
+        assert b"hello world" == jws.decode(msg, pub_key, algorithms=["ES256"])
+
     def test_decode_algorithm_param_should_be_case_sensitive(self, jws):
         example_jws = (
             "eyJhbGciOiJoczI1NiIsInR5cCI6IkpXVCJ9"  # alg = hs256