diff --git a/Lib/pickle.py b/Lib/pickle.py
index ec19e24..e365bd1 100644
--- a/Lib/pickle.py
+++ b/Lib/pickle.py
@@ -787,9 +787,8 @@
         if name is None:
             name = obj.__name__
 
-        try:
-            module = obj.__module__
-        except AttributeError:
+        module = getattr(obj, "__module__", None)
+        if module is None:
             module = whichmodule(obj, name)
 
         try:
@@ -876,6 +875,10 @@
     Return a module name.
     If the function cannot be found, return "__main__".
     """
+    # Python functions should always get an __module__ from their globals.
+    mod = getattr(func, "__module__", None)
+    if mod is not None:
+        return mod
     if func in classmap:
         return classmap[func]
 
diff --git a/Lib/test/test_funcattrs.py b/Lib/test/test_funcattrs.py
index 3dc888c..2c31d36 100644
--- a/Lib/test/test_funcattrs.py
+++ b/Lib/test/test_funcattrs.py
@@ -9,6 +9,10 @@
     'my docstring'
     pass
 
+# __module__ is a special attribute
+verify(b.__module__ == __name__)
+verify(verify.__module__ == "test.test_support")
+
 # setting attributes on functions
 try:
     b.publish