diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index 2210e185..34276ca6 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -226,9 +226,12 @@ class Script(object):
 
     def _simple_complete(self, path, dot, like):
         if not path and not dot:
+            scope = self._parser.user_scope()
+            if not scope.is_scope():  # Might be a flow (if/while/etc).
+                scope = scope.get_parent_scope()
             names_dicts = global_names_dict_generator(
                 self._evaluator,
-                er.wrap(self._evaluator, self._parser.user_scope()),
+                er.wrap(self._evaluator, scope),
                 self._pos
             )
             completions = []
diff --git a/jedi/evaluate/finder.py b/jedi/evaluate/finder.py
index 3f12e725..e43020e0 100644
--- a/jedi/evaluate/finder.py
+++ b/jedi/evaluate/finder.py
@@ -36,7 +36,7 @@ def filter_definition_names(names, origin, position=None):
     # Just calculate the scope from the first
     stmt = names[0].get_definition()
     scope = stmt.get_parent_scope()
-    if isinstance(stmt, (pr.CompFor, pr.Lambda, pr.GlobalStmt)):
+    if isinstance(stmt, (pr.CompFor, pr.Lambda)):
         return names
 
     if not (isinstance(scope, er.FunctionExecution)
@@ -377,7 +377,13 @@ def _name_to_types(evaluator, name, scope):
     elif isinstance(typ, pr.Import):
         types += imports.ImportWrapper(evaluator, name).follow()
     elif isinstance(typ, pr.GlobalStmt):
-        types += evaluator.find_types(typ.get_parent_scope(), str(name))
+        # TODO theoretically we shouldn't be using search_global here, it
+        # doesn't make sense, because it's a local search (for that name)!
+        # However, globals are not that important and resolving them doesn't
+        # guarantee correctness in any way, because we don't check for when
+        # something is executed.
+        types += evaluator.find_types(typ.get_parent_scope(), str(name),
+                                      search_global=True)
     elif isinstance(typ, pr.TryStmt):
         # TODO an exception can also be a tuple. Check for those.
         # TODO check for types that are not classes and add it to
diff --git a/jedi/evaluate/representation.py b/jedi/evaluate/representation.py
index 7480ee73..fe6c08fb 100644
--- a/jedi/evaluate/representation.py
+++ b/jedi/evaluate/representation.py
@@ -824,6 +824,16 @@ class FunctionExecution(Executed):
         return "<%s of %s>" % (type(self).__name__, self.base)
 
 
+class GlobalName(helpers.FakeName):
+    def __init__(self, name):
+        """
+        We need to mark global names somehow. Otherwise they are just normal
+        names that are not definitions.
+        """
+        super(GlobalName, self).__init__(name.value, name.parent,
+                                         name.start_pos, is_definition=True)
+
+
 class ModuleWrapper(use_metaclass(CachedMetaClass, pr.Module, Wrapper)):
     def __init__(self, evaluator, module):
         self._evaluator = evaluator
@@ -847,7 +857,7 @@ class ModuleWrapper(use_metaclass(CachedMetaClass, pr.Module, Wrapper)):
         for star_module in self.star_imports():
             yield star_module.names_dict
 
-        yield dict((str(n), [n]) for n in self.base.global_names)
+        yield dict((str(n), [GlobalName(n)]) for n in self.base.global_names)
         yield self._sub_modules_dict()
 
     @cache_star_import
diff --git a/jedi/parser/__init__.py b/jedi/parser/__init__.py
index 6c8e7e6b..f361d4a8 100644
--- a/jedi/parser/__init__.py
+++ b/jedi/parser/__init__.py
@@ -147,7 +147,7 @@ class Parser(object):
         # We need to check raw_node always, because the same node can be
         # returned by convert multiple times.
         if symbol == 'global_stmt':
-            self.global_names += new_node.get_defined_names()
+            self.global_names += new_node.get_global_names()
         elif isinstance(new_node, pt.Lambda):
             new_node.names_dict = self.scope_names_stack.pop()
         elif isinstance(new_node, (pt.ClassOrFunc, pt.Module)) \
diff --git a/jedi/parser/tree.py b/jedi/parser/tree.py
index 8c3e5e22..4b925925 100644
--- a/jedi/parser/tree.py
+++ b/jedi/parser/tree.py
@@ -1128,6 +1128,9 @@ class GlobalStmt(KeywordStatement):
     __slots__ = ()
 
     def get_defined_names(self):
+        return []
+
+    def get_global_names(self):
         return self.children[1::2]