diff --git a/jedi/_compatibility.py b/jedi/_compatibility.py
index 387e4b18..d51356d6 100644
--- a/jedi/_compatibility.py
+++ b/jedi/_compatibility.py
@@ -7,6 +7,7 @@ import os
 import re
 import pkgutil
 import warnings
+import inspect
 try:
     import importlib
 except ImportError:
@@ -174,7 +175,6 @@ def _iter_modules(paths, prefix=''):
 
         yielded = {}
 
-        import inspect
         try:
             filenames = os.listdir(importer.path)
         except OSError:
@@ -457,3 +457,14 @@ def pickle_load(file):
 
 def pickle_dump(data, file):
     pickle.dump(data, file, protocol=_PICKLE_PROTOCOL)
+
+
+try:
+    from inspect import Parameter
+except ImportError:
+    class Parameter(object):
+        POSITIONAL_ONLY = object()
+        POSITIONAL_OR_KEYWORD = object()
+        VAR_POSITIONAL = object()
+        KEYWORD_ONLY = object()
+        VAR_KEYWORD = object()
diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index dcf18ee3..1d49b587 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -2,6 +2,7 @@ from parso.python import token
 from parso.python import tree
 from parso.tree import search_ancestor, Leaf
 
+from jedi._compatibility import Parameter
 from jedi import debug
 from jedi import settings
 from jedi.api import classes
@@ -18,17 +19,9 @@ def get_call_signature_param_names(call_signatures):
     for call_sig in call_signatures:
         for p in call_sig.params:
             # Allow protected access, because it's a public API.
-            tree_name = p._name.tree_name
-            # Compiled modules typically don't allow keyword arguments.
-            if tree_name is not None:
-                # Allow access on _definition here, because it's a
-                # public API and we don't want to make the internal
-                # Name object public.
-                tree_param = tree.search_ancestor(tree_name, 'param')
-                if tree_param.star_count != 0:  # no *args/**kwargs
-                    continue
-
-            yield p._name
+            if p._name.get_kind() in (Parameter.POSITIONAL_OR_KEYWORD,
+                                      Parameter.KEYWORD_ONLY):
+                yield p._name
 
 
 def filter_names(evaluator, completion_names, stack, like_name):
diff --git a/jedi/evaluate/compiled/access.py b/jedi/evaluate/compiled/access.py
index 171873ac..97a8dd0b 100644
--- a/jedi/evaluate/compiled/access.py
+++ b/jedi/evaluate/compiled/access.py
@@ -99,7 +99,10 @@ def safe_getattr(obj, name, default=_sentinel):
     return attr
 
 
-SignatureParam = namedtuple('SignatureParam', 'name has_default default has_annotation annotation')
+SignatureParam = namedtuple(
+    'SignatureParam',
+    'name has_default default has_annotation annotation kind_name'
+)
 
 
 def compiled_objects_cache(attribute_name):
@@ -413,6 +416,7 @@ class DirectObjectAccess(object):
                 default=self._create_access_path(p.default),
                 has_annotation=p.annotation is not p.empty,
                 annotation=self._create_access_path(p.annotation),
+                kind_name=str(p.kind)
             ) for p in signature.parameters.values()
         ]
 
diff --git a/jedi/evaluate/compiled/context.py b/jedi/evaluate/compiled/context.py
index 25949af7..f81509d7 100644
--- a/jedi/evaluate/compiled/context.py
+++ b/jedi/evaluate/compiled/context.py
@@ -5,7 +5,7 @@ import re
 from functools import partial
 
 from jedi import debug
-from jedi._compatibility import force_unicode
+from jedi._compatibility import force_unicode, Parameter
 from jedi.cache import underscore_memoization, memoize_method
 from jedi.evaluate.filters import AbstractFilter, AbstractNameDefinition, \
     ContextNameMixin
@@ -248,6 +248,12 @@ class SignatureParamName(AbstractNameDefinition):
     def string_name(self):
         return self._signature_param.name
 
+    def get_kind(self):
+        return getattr(Parameter, self._signature_param.kind_name)
+
+    def is_keyword_param(self):
+        return self._signature_param
+
     def infer(self):
         p = self._signature_param
         evaluator = self.parent_context.evaluator
@@ -267,6 +273,9 @@ class UnresolvableParamName(AbstractNameDefinition):
         self.parent_context = compiled_obj.parent_context
         self.string_name = name
 
+    def get_kind(self):
+        return Parameter.POSITIONAL_ONLY
+
     def infer(self):
         return ContextSet()
 
diff --git a/jedi/evaluate/filters.py b/jedi/evaluate/filters.py
index db66e48a..4294f2a6 100644
--- a/jedi/evaluate/filters.py
+++ b/jedi/evaluate/filters.py
@@ -6,7 +6,7 @@ from abc import abstractmethod
 
 from parso.tree import search_ancestor
 
-from jedi._compatibility import use_metaclass
+from jedi._compatibility import use_metaclass, Parameter
 from jedi.cache import memoize_method
 from jedi.evaluate import flow_analysis
 from jedi.evaluate.base_context import ContextSet, Context
@@ -122,6 +122,22 @@ class ParamName(AbstractTreeName):
         self.parent_context = parent_context
         self.tree_name = tree_name
 
+    def get_kind(self):
+        tree_param = search_ancestor(self.tree_name, 'param')
+        if tree_param.star_count == 1:  # *args
+            return Parameter.VAR_POSITIONAL
+        if tree_param.star_count == 2:  # **kwargs
+            return Parameter.VAR_KEYWORD
+
+        parent = tree_param.parent
+        for p in parent.children:
+            if p.type == 'param':
+                if p.star_count:
+                    return Parameter.KEYWORD_ONLY
+                if p == tree_param:
+                    break
+        return Parameter.POSITIONAL_OR_KEYWORD
+
     def infer(self):
         return self.get_param().infer()