diff --git a/jose/jwt.py b/jose/jwt.py
index bffed256..9a0396dc 100644
--- a/jose/jwt.py
+++ b/jose/jwt.py
@@ -12,7 +12,7 @@
 from .utils import timedelta_total_seconds
 
 
-def encode(claims, key, algorithm=None):
+def encode(claims, key, algorithm=None, headers=None):
     """Encodes a claims set and returns a JWT string.
 
     JWTs are JWS signed objects with a few reserved claims.
@@ -20,11 +20,11 @@ def encode(claims, key, algorithm=None):
     Args:
         claims (dict): A claims set to sign
         key (str): The key to use for signing the claim set
+        algorithm (str, optional): The algorithm to use for signing the
+            the claims.  Defaults to HS256.
         headers (dict, optional): A set of headers that will be added to
             the default headers.  Any headers that are added as additional
             headers will override the default headers.
-        algorithm (str, optional): The algorithm to use for signing the
-            the claims.  Defaults to HS256.
 
     Returns:
         str: The string representation of the header, claims, and signature.
@@ -46,9 +46,9 @@ def encode(claims, key, algorithm=None):
             claims[time_claim] = timegm(claims[time_claim].utctimetuple())
 
     if algorithm:
-        return jws.sign(claims, key, algorithm=algorithm)
+        return jws.sign(claims, key, headers=headers, algorithm=algorithm)
 
-    return jws.sign(claims, key)
+    return jws.sign(claims, key, headers=headers)
 
 
 def decode(token, key, algorithms=None, options=None, audience=None, issuer=None):
diff --git a/tests/test_jwt.py b/tests/test_jwt.py
index acc64210..05926b58 100644
--- a/tests/test_jwt.py
+++ b/tests/test_jwt.py
@@ -20,6 +20,12 @@ def claims():
 def key():
     return 'secret'
 
+@pytest.fixture
+def headers():
+    headers = {
+        'kid': 'my-key-id',
+    }
+    return headers
 
 class TestJWT:
 
@@ -28,6 +34,19 @@ def test_non_default_alg(self, claims, key):
         decoded = jwt.decode(encoded, key, algorithms='HS384')
         assert claims == decoded
 
+    def test_non_default_alg_positional_bwcompat(self, claims, key):
+        encoded = jwt.encode(claims, key, 'HS384')
+        decoded = jwt.decode(encoded, key, 'HS384')
+        assert claims == decoded
+
+    def test_non_default_headers(self, claims, key, headers):
+        encoded = jwt.encode(claims, key, headers=headers)
+        decoded = jwt.decode(encoded, key)
+        assert claims == decoded
+        all_headers = jwt.get_unverified_headers(encoded)
+        for k, v in headers.items():
+            assert all_headers[k] == v
+
     def test_encode(self, claims, key):
 
         expected = (