diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index d8451662..25b0d836 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -143,7 +143,7 @@ class Script(object):
         if not dot:
             # add named params
             for call_def in self.call_signatures():
-                if not call_def.module.is_builtin():
+                if not isinstance(call_def.module, compiled.PyObject):
                     for p in call_def.params:
                         completions.append((p.get_name(), p))
 
diff --git a/jedi/evaluate/__init__.py b/jedi/evaluate/__init__.py
index 8ab470db..36a410e7 100644
--- a/jedi/evaluate/__init__.py
+++ b/jedi/evaluate/__init__.py
@@ -282,8 +282,8 @@ class Evaluator(object):
                     result += self.eval_call(call)
                 elif call == '*':
                     if [r for r in result if isinstance(r, iterable.Array)
-                       or isinstance(r, er.Instance)
-                       and str(r.name) == 'str']:
+                            or isinstance(r, compiled.PyObject)
+                            and isinstance(r.obj, (str, unicode))]:
                         # if it is an iterable, ignore * operations
                         next(calls_iterator)
         return set(result)
@@ -452,8 +452,8 @@ def filter_private_variable(scope, call_scope, var_name):
     if isinstance(var_name, (str, unicode)) and isinstance(scope, er.Instance)\
             and var_name.startswith('__') and not var_name.endswith('__'):
         s = call_scope.get_parent_until((pr.Class, er.Instance))
-        if not isinstance(scope.base, compiled.PyObject):
-            if s != scope and s != scope.base.base:
+        if s != scope and (isinstance(scope.base, compiled.PyObject)
+                           or s != scope.base.base):
                 return True
     return False
 
diff --git a/jedi/evaluate/compiled/__init__.py b/jedi/evaluate/compiled/__init__.py
index fbb9e1de..78dafecc 100644
--- a/jedi/evaluate/compiled/__init__.py
+++ b/jedi/evaluate/compiled/__init__.py
@@ -109,6 +109,7 @@ class PyObject(Base):
         for name in dir(self._cls().obj):
             f = fake.get_faked(module.obj, self.obj, name)
             if f:
+                f.parent = self
                 faked_subscopes.append(f)
         return faked_subscopes
 
diff --git a/jedi/evaluate/helpers.py b/jedi/evaluate/helpers.py
index 77a9e70a..b298d8bb 100644
--- a/jedi/evaluate/helpers.py
+++ b/jedi/evaluate/helpers.py
@@ -163,9 +163,10 @@ class FakeSubModule():
 
 
 class FakeStatement(pr.Statement):
-    def __init__(self, token_list):
+    def __init__(self, expression_list):
         p = 0, 0
-        super(FakeStatement, self).__init__(FakeSubModule, token_list, p, p)
+        super(FakeStatement, self).__init__(FakeSubModule, expression_list, p, p)
+        self._expression_list = expression_list
 
 
 class FakeName(pr.Name):
diff --git a/jedi/evaluate/iterable.py b/jedi/evaluate/iterable.py
index 842cac82..63aeb801 100644
--- a/jedi/evaluate/iterable.py
+++ b/jedi/evaluate/iterable.py
@@ -96,6 +96,8 @@ class Array(use_metaclass(CachedMetaClass, pr.Base)):
                     str_key = key.value
                 elif isinstance(key, pr.Name):
                     str_key = str(key)
+                else:
+                    continue
 
                 if mixed_index == str_key:
                     index = i