diff -r ad92e63de42c Lib/inspect.py
--- a/Lib/inspect.py	Thu Feb 20 23:26:12 2014 +0100
+++ b/Lib/inspect.py	Thu Feb 20 19:51:56 2014 -0500
@@ -1828,8 +1828,17 @@
 
     if self_parameter is not None:
         assert parameters
-        if getattr(obj, '__self__', None) and skip_bound_arg:
-            # strip off self, it's already been bound
+        self_attr = getattr(obj, '__self__', None)
+        self_attr_ismod = ismodule(self_attr)
+        if (self_attr is not None
+                and (self_attr_ismod
+                        or (not self_attr_ismod and skip_bound_arg))):
+            # Strip the bound argument. Couple of notes:
+            #
+            # 1. We *always* strip first bound argument if
+            #    it is a module.
+            # 2. We don't strip first bound argument if
+            #    skip_bound_arg is False.
             parameters.pop(0)
         else:
             # for builtins, self parameter is always positional-only!
diff -r ad92e63de42c Lib/test/test_inspect.py
--- a/Lib/test/test_inspect.py	Thu Feb 20 23:26:12 2014 +0100
+++ b/Lib/test/test_inspect.py	Thu Feb 20 19:51:56 2014 -0500
@@ -643,6 +643,13 @@
         self.assertFullArgSpecEquals(_pickle.Pickler(io.BytesIO()).dump,
                                      args_e=['self', 'obj'], formatted='(self, obj)')
 
+        self.assertFullArgSpecEquals(
+             os.stat,
+             args_e=['path'],
+             kwonlyargs_e=['dir_fd', 'follow_symlinks'],
+             kwonlydefaults_e={'dir_fd': None, 'follow_symlinks': True},
+             formatted='(path, *, dir_fd=None, follow_symlinks=True)')
+
     @cpython_only
     @unittest.skipIf(MISSING_C_DOCSTRINGS,
                      "Signature information for builtins requires docstrings")