diff --git a/jwcrypto/jwk.py b/jwcrypto/jwk.py
index c5f36a7..977bd62 100644
--- a/jwcrypto/jwk.py
+++ b/jwcrypto/jwk.py
@@ -180,10 +180,13 @@ class ParmType(Enum):
                          'deriveBits': 'Derive bits not to be used as a key'}
 """Registry of allowed operations"""
 
+# P-256K is an alias for 'secp256k1' to handle compatibility with some
+# implementation using this old drafting name
 JWKpycaCurveMap = {'secp256r1': 'P-256',
                    'secp384r1': 'P-384',
                    'secp521r1': 'P-521',
-                   'secp256k1': 'secp256k1'}
+                   'secp256k1': 'secp256k1',
+                   'secp256k1': 'P-256K'}
 
 
 class InvalidJWKType(JWException):
@@ -400,7 +403,7 @@ def _get_curve_by_name(self, name):
             return ec.SECP384R1()
         elif name == 'P-521':
             return ec.SECP521R1()
-        elif name == 'secp256k1':
+        elif name == 'secp256k1' or name == 'P-256K':
             return ec.SECP256K1()
         elif name in _OKP_CURVES_TABLE:
             return name