diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index b8ed3524..394d8526 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -159,7 +159,7 @@ class Script(object):
         if not dot:
             # add named params
             for call_sig in self.call_signatures():
-                # allow protected access, because it's a public API.
+                # Allow protected access, because it's a public API.
                 module = call_sig._definition.get_parent_until()
                 # Compiled modules typically don't allow keyword arguments.
                 if not isinstance(module, compiled.CompiledObject):
@@ -167,8 +167,8 @@ class Script(object):
                         # Allow access on _definition here, because it's a
                         # public API and we don't want to make the internal
                         # Name object public.
-                        if p._definition.stars == 0:  # no *args/**kwargs
-                            completions.append((p._definition.get_name(), p))
+                        if p._definition.get_definition().stars == 0:  # no *args/**kwargs
+                            completions.append((p._definition.parent, p))
 
             if not path and not isinstance(user_stmt, pr.Import):
                 # add keywords
diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index 983400a1..8262fa3a 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -385,7 +385,7 @@ class BaseDefinition(object):
                 params = sub.params[1:]  # ignore self
             except KeyError:
                 return []
-        return [_Param(self._evaluator, p) for p in params]
+        return [_Param(self._evaluator, p.get_name().names[-1]) for p in params]
 
     def parent(self):
         if isinstance(self._definition, compiled.CompiledObject):
@@ -575,6 +575,8 @@ class Definition(use_metaclass(CachedMetaClass, BaseDefinition)):
     """
     def __init__(self, evaluator, definition):
         super(Definition, self).__init__(evaluator, definition, definition.start_pos)
+        if not isinstance(definition, pr.NamePart):
+            raise NotImplementedError(definition)
 
     @property
     @underscore_memoization