diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index ade9f6d8..c620a123 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -698,9 +698,17 @@ class CallSignature(Definition):
             for i, param in enumerate(self.params):
                 if self._key_name == param.name:
                     return i
-            return None
+            if self.params and self.params[-1]._definition.stars == 2:
+                return i
+            else:
+                return None
 
         if self._index >= len(self.params):
+
+            for i, param in enumerate(self.params):
+                # *args case
+                if param._definition.stars == 1:
+                    return i
             return None
         return self._index
 
diff --git a/test/test_api/test_call_signatures.py b/test/test_api/test_call_signatures.py
index 91584982..bb049a9d 100644
--- a/test/test_api/test_call_signatures.py
+++ b/test/test_api/test_call_signatures.py
@@ -243,3 +243,17 @@ def test_signature_index():
         return Script(source).call_signatures()[0]
 
     assert get('sorted([], key=a').index == 2
+    assert get('sorted([], no_key=a').index is None
+
+    args_func = 'def foo(*kwargs): pass\n'
+    assert get(args_func + 'foo(a').index == 0
+    assert get(args_func + 'foo(a, b').index == 0
+
+    kwargs_func = 'def foo(**kwargs): pass\n'
+    assert get(kwargs_func + 'foo(a=2').index == 0
+    assert get(kwargs_func + 'foo(a=2, b=2').index == 0
+
+    both = 'def foo(*args, **kwargs): pass\n'
+    assert get(both + 'foo(a=2').index == 1
+    assert get(both + 'foo(a=2, b=2').index == 1
+    assert get(both + 'foo(a, b, c').index == 0