diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index e5c789ea..79756a78 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -142,7 +142,7 @@ class BaseDefinition(object):
             stripped = stripped.parent
         if isinstance(stripped, pr.Name):
             stripped = stripped.parent
-        return type(stripped).__name__.lower()
+        return type(stripped).__name__.lower().replace('wrapper', '')
 
     def _path(self):
         """The module path."""
diff --git a/jedi/evaluate/finder.py b/jedi/evaluate/finder.py
index 7d6a13e9..02784444 100644
--- a/jedi/evaluate/finder.py
+++ b/jedi/evaluate/finder.py
@@ -206,6 +206,8 @@ class NameFinder(object):
                     typ = er.Class(evaluator, typ)
                 elif isinstance(typ, pr.Function):
                     typ = er.Function(evaluator, typ)
+                elif isinstance(typ, pr.Module):
+                    typ = er.ModuleWrapper(evaluator, typ)
                 if typ.isinstance(er.Function) and resolve_decorator:
                     typ = typ.get_decorated_func()
                 types.append(typ)
diff --git a/jedi/evaluate/imports.py b/jedi/evaluate/imports.py
index 2f868d85..568c6c27 100644
--- a/jedi/evaluate/imports.py
+++ b/jedi/evaluate/imports.py
@@ -473,7 +473,13 @@ def follow_imports(evaluator, scopes):
     result = []
     for s in scopes:
         if isinstance(s, pr.Import):
-            result += ImportWrapper(evaluator, s).follow()
+            for r in ImportWrapper(evaluator, s).follow():
+                if isinstance(r, pr.Module) and not isinstance(r,
+                    StarImportModule):
+                    # TODO This check is strange and feels wrong somehow. Change it.
+                    from jedi.evaluate import representation as er
+                    r = er.ModuleWrapper(evaluator, r)
+                result.append(r)
         else:
             result.append(s)
     return result
diff --git a/jedi/evaluate/representation.py b/jedi/evaluate/representation.py
index c9b886d4..fc87b17a 100644
--- a/jedi/evaluate/representation.py
+++ b/jedi/evaluate/representation.py
@@ -521,3 +521,23 @@ class FunctionExecution(Executable):
 
     def __repr__(self):
         return "<%s of %s>" % (type(self).__name__, self.base)
+
+
+class ModuleWrapper(pr.Module):
+    def __init__(self, evaluator, module):
+        self._evaluator = evaluator
+        self._module = module
+
+    @memoize_default()
+    def get_defined_names(self):
+        names = ['__file__', '__package__', '__doc__', '__name__', '__version__']
+        # All the additional module attributes are strings.
+        parent = Instance(self._evaluator, compiled.create(self._evaluator, str))
+        module_attributes = [helpers.FakeName(n, parent) for n in names]
+        return self._module.get_defined_names() + module_attributes
+
+    def __getattr__(self, name):
+        return getattr(self._module, name)
+
+    def __repr__(self):
+        return "<%s: %s>" % (type(self).__name__, self._module)
diff --git a/test/completion/imports.py b/test/completion/imports.py
index cd5193a9..79072c4b 100644
--- a/test/completion/imports.py
+++ b/test/completion/imports.py
@@ -46,8 +46,8 @@ def scope_nested():
     #? ['sqrt']
     import_tree.pkg.sqrt
 
-    #? ['a', 'pkg']
-    import_tree.
+    #? ['pkg']
+    import_tree.p
 
     #? float()
     import_tree.pkg.mod1.a
@@ -317,3 +317,12 @@ else:
     a = not_existing_import
 #? 
 a
+
+# -----------------
+# magic methods
+# -----------------
+
+def magic_method():
+    import keyword
+    #? ['__file__']
+    keyword.__file__