diff -r f6792f734fcc Doc/library/enum.rst
--- a/Doc/library/enum.rst	Sun Sep 29 00:28:55 2013 +1000
+++ b/Doc/library/enum.rst	Sun Sep 29 00:54:43 2013 +1000
@@ -536,19 +536,9 @@
 the normal :class:`Enum` invariants (such as not being comparable to other
 enumerations)::
 
-    >>> class OrderedEnum(Enum):
-    ...     def __ge__(self, other):
-    ...         if self.__class__ is other.__class__:
-    ...             return self.value >= other.value
-    ...         return NotImplemented
-    ...     def __gt__(self, other):
-    ...         if self.__class__ is other.__class__:
-    ...             return self.value > other.value
-    ...         return NotImplemented
-    ...     def __le__(self, other):
-    ...         if self.__class__ is other.__class__:
-    ...             return self.value <= other.value
-    ...         return NotImplemented
+    >>> import functools
+    >>> @functools.total_ordering
+    ... class OrderedEnum(Enum):
     ...     def __lt__(self, other):
     ...         if self.__class__ is other.__class__:
     ...             return self.value < other.value
diff -r f6792f734fcc Lib/functools.py
--- a/Lib/functools.py	Sun Sep 29 00:28:55 2013 +1000
+++ b/Lib/functools.py	Sun Sep 29 00:54:43 2013 +1000
@@ -89,21 +89,65 @@
 ### total_ordering class decorator
 ################################################################################
 
+def _not_op(op, other):
+    # "not a < b" handles "a >= b"
+    # "not a <= b" handles "a > b"
+    # "not a >= b" handles "a < b"
+    # "not a > b" handles "a <= b"
+    op_result = op(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result
+
+def _op_or_eq(op, self, other):
+    # "a < b or a == b" handles "a <= b"
+    # "a > b or a == b" handles "a >= b"
+    op_result = op(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return op_result or self == other
+
+def _not_op_and_not_eq(op, self, other):
+    # "not (a < b or a == b)" handles "a > b"
+    # "not a < b and a != b" is equivalent
+    # "not (a > b or a == b)" handles "a < b"
+    # "not a > b and a != b" is equivalent
+    op_result = op(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result and self != other
+
+def _not_op_or_eq(op, self, other):
+    # "not a <= b or a == b" handles "a >= b"
+    # "not a >= b or a == b" handles "a <= b"
+    op_result = op(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return not op_result or self == other
+
+def _op_and_not_eq(op, self, other):
+    # "a <= b and not a == b" handles "a < b"
+    # "a >= b and not a == b" handles "a > b"
+    op_result = op(other)
+    if op_result is NotImplemented:
+        return NotImplemented
+    return op_result and self != other
+
 def total_ordering(cls):
     """Class decorator that fills in missing ordering methods"""
     convert = {
-        '__lt__': [('__gt__', lambda self, other: not (self < other or self == other)),
-                   ('__le__', lambda self, other: self < other or self == other),
-                   ('__ge__', lambda self, other: not self < other)],
-        '__le__': [('__ge__', lambda self, other: not self <= other or self == other),
-                   ('__lt__', lambda self, other: self <= other and not self == other),
-                   ('__gt__', lambda self, other: not self <= other)],
-        '__gt__': [('__lt__', lambda self, other: not (self > other or self == other)),
-                   ('__ge__', lambda self, other: self > other or self == other),
-                   ('__le__', lambda self, other: not self > other)],
-        '__ge__': [('__le__', lambda self, other: (not self >= other) or self == other),
-                   ('__gt__', lambda self, other: self >= other and not self == other),
-                   ('__lt__', lambda self, other: not self >= other)]
+        '__lt__': [('__gt__', lambda self, other: _not_op_and_not_eq(self.__lt__, self, other)),
+                   ('__le__', lambda self, other: _op_or_eq(self.__lt__, self, other)),
+                   ('__ge__', lambda self, other: _not_op(self.__lt__, other))],
+        '__le__': [('__ge__', lambda self, other: _not_op_or_eq(self.__le__, self, other)),
+                   ('__lt__', lambda self, other: _op_and_not_eq(self.__le__, self, other)),
+                   ('__gt__', lambda self, other: _not_op(self.__le__, other))],
+        '__gt__': [('__lt__', lambda self, other: _not_op_and_not_eq(self.__gt__, self, other)),
+                   ('__ge__', lambda self, other: _op_or_eq(self.__gt__, self, other)),
+                   ('__le__', lambda self, other: _not_op(self.__gt__, other))],
+        '__ge__': [('__le__', lambda self, other: _not_op_or_eq(self.__ge__, self, other)),
+                   ('__gt__', lambda self, other: _op_and_not_eq(self.__ge__, self, other)),
+                   ('__lt__', lambda self, other: _not_op(self.__ge__, other))]
     }
     # Find user-defined comparisons (not those inherited from object).
     roots = [op for op in convert if getattr(cls, op, None) is not getattr(object, op, None)]
diff -r f6792f734fcc Lib/test/test_enum.py
--- a/Lib/test/test_enum.py	Sun Sep 29 00:28:55 2013 +1000
+++ b/Lib/test/test_enum.py	Sun Sep 29 00:54:43 2013 +1000
@@ -2,6 +2,7 @@
 import unittest
 from collections import OrderedDict
 from pickle import dumps, loads, PicklingError
+from functools import total_ordering
 from enum import Enum, IntEnum, unique
 
 # for pickle tests
@@ -999,23 +1000,13 @@
         self.assertEqual(list(map(int, Color)), [1, 2, 3])
 
     def test_ordered_mixin(self):
+        @total_ordering
         class OrderedEnum(Enum):
-            def __ge__(self, other):
-                if self.__class__ is other.__class__:
-                    return self._value_ >= other._value_
-                return NotImplemented
-            def __gt__(self, other):
-                if self.__class__ is other.__class__:
-                    return self._value_ > other._value_
-                return NotImplemented
-            def __le__(self, other):
-                if self.__class__ is other.__class__:
-                    return self._value_ <= other._value_
-                return NotImplemented
             def __lt__(self, other):
                 if self.__class__ is other.__class__:
                     return self._value_ < other._value_
                 return NotImplemented
+        # Simple checks
         class Grade(OrderedEnum):
             A = 5
             B = 4
@@ -1027,6 +1018,22 @@
         self.assertLess(Grade.D, Grade.A)
         self.assertGreaterEqual(Grade.B, Grade.B)
 
+        # Checks between ordered enums
+        class BinaryGrade(OrderedEnum):
+            Pass = 2
+            Fail = 1
+
+        self.assertNotEqual(Grade.D, BinaryGrade.Pass)
+        self.assertNotEqual(Grade.F, BinaryGrade.Fail)
+        with self.assertRaises(TypeError):
+            Grade.A > BinaryGrade.Pass
+        with self.assertRaises(TypeError):
+            Grade.A >= BinaryGrade.Pass
+        with self.assertRaises(TypeError):
+            Grade.A <= BinaryGrade.Pass
+        with self.assertRaises(TypeError):
+            Grade.A < BinaryGrade.Pass
+
     def test_extending2(self):
         class Shade(Enum):
             def shade(self):
diff -r f6792f734fcc Lib/test/test_functools.py
--- a/Lib/test/test_functools.py	Sun Sep 29 00:28:55 2013 +1000
+++ b/Lib/test/test_functools.py	Sun Sep 29 00:54:43 2013 +1000
@@ -584,6 +584,7 @@
         self.assertTrue(A(2) >= A(1))
         self.assertTrue(A(2) <= A(2))
         self.assertTrue(A(2) >= A(2))
+        self.assertFalse(A(1) > A(2))
 
     def test_total_ordering_le(self):
         @functools.total_ordering
@@ -600,6 +601,7 @@
         self.assertTrue(A(2) >= A(1))
         self.assertTrue(A(2) <= A(2))
         self.assertTrue(A(2) >= A(2))
+        self.assertFalse(A(1) >= A(2))
 
     def test_total_ordering_gt(self):
         @functools.total_ordering
@@ -616,6 +618,7 @@
         self.assertTrue(A(2) >= A(1))
         self.assertTrue(A(2) <= A(2))
         self.assertTrue(A(2) >= A(2))
+        self.assertFalse(A(2) < A(1))
 
     def test_total_ordering_ge(self):
         @functools.total_ordering
@@ -632,6 +635,7 @@
         self.assertTrue(A(2) >= A(1))
         self.assertTrue(A(2) <= A(2))
         self.assertTrue(A(2) >= A(2))
+        self.assertFalse(A(2) <= A(1))
 
     def test_total_ordering_no_overwrite(self):
         # new methods should not overwrite existing
@@ -651,22 +655,112 @@
             class A:
                 pass
 
-    def test_bug_10042(self):
+    def test_type_error_when_not_implemented(self):
+        # bug 10042; ensure stack overflow does not occur
+        # when decorated types return NotImplemented
         @functools.total_ordering
-        class TestTO:
+        class ImplementsLessThan:
             def __init__(self, value):
                 self.value = value
             def __eq__(self, other):
-                if isinstance(other, TestTO):
+                if isinstance(other, ImplementsLessThan):
                     return self.value == other.value
                 return False
             def __lt__(self, other):
-                if isinstance(other, TestTO):
+                if isinstance(other, ImplementsLessThan):
                     return self.value < other.value
-                raise TypeError
-        with self.assertRaises(TypeError):
-            TestTO(8) <= ()
+                return NotImplemented
 
+        @functools.total_ordering
+        class ImplementsGreaterThan:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, ImplementsGreaterThan):
+                    return self.value == other.value
+                return False
+            def __gt__(self, other):
+                if isinstance(other, ImplementsGreaterThan):
+                    return self.value > other.value
+                return NotImplemented
+
+        @functools.total_ordering
+        class ImplementsLessThanEqualTo:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, ImplementsLessThanEqualTo):
+                    return self.value == other.value
+                return False
+            def __le__(self, other):
+                if isinstance(other, ImplementsLessThanEqualTo):
+                    return self.value <= other.value
+                return NotImplemented
+
+        @functools.total_ordering
+        class ImplementsGreaterThanEqualTo:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, ImplementsGreaterThanEqualTo):
+                    return self.value == other.value
+                return False
+            def __ge__(self, other):
+                if isinstance(other, ImplementsGreaterThanEqualTo):
+                    return self.value >= other.value
+                return NotImplemented
+
+        @functools.total_ordering
+        class ComparatorNotImplemented:
+            def __init__(self, value):
+                self.value = value
+            def __eq__(self, other):
+                if isinstance(other, ComparatorNotImplemented):
+                    return self.value == other.value
+                return False
+            def __lt__(self, other):
+                return NotImplemented
+
+        with self.subTest("LT < 1"), self.assertRaises(TypeError):
+            ImplementsLessThan(-1) < 1
+
+        with self.subTest("LT < LE"), self.assertRaises(TypeError):
+            ImplementsLessThan(0) < ImplementsLessThanEqualTo(0)
+
+        with self.subTest("LT < GT"), self.assertRaises(TypeError):
+            ImplementsLessThan(1) < ImplementsGreaterThan(1)
+
+        with self.subTest("LE <= LT"), self.assertRaises(TypeError):
+            ImplementsLessThanEqualTo(2) <= ImplementsLessThan(2)
+
+        with self.subTest("LE <= GE"), self.assertRaises(TypeError):
+            ImplementsLessThanEqualTo(3) <= ImplementsGreaterThanEqualTo(3)
+
+        with self.subTest("GT > GE"), self.assertRaises(TypeError):
+            ImplementsGreaterThan(4) > ImplementsGreaterThanEqualTo(4)
+
+        with self.subTest("GT > LT"), self.assertRaises(TypeError):
+            ImplementsGreaterThan(5) > ImplementsLessThan(5)
+
+        with self.subTest("GE >= GT"), self.assertRaises(TypeError):
+            ImplementsGreaterThanEqualTo(6) >= ImplementsGreaterThan(6)
+
+        with self.subTest("GE >= LE"), self.assertRaises(TypeError):
+            ImplementsGreaterThanEqualTo(7) >= ImplementsLessThanEqualTo(7)
+
+        with self.subTest("GE when equal"):
+            a = ComparatorNotImplemented(8)
+            b = ComparatorNotImplemented(8)
+            self.assertEqual(a, b)
+            with self.assertRaises(TypeError):
+                a >= b
+
+        with self.subTest("LE when equal"):
+            a = ComparatorNotImplemented(9)
+            b = ComparatorNotImplemented(9)
+            self.assertEqual(a, b)
+            with self.assertRaises(TypeError):
+                a <= b
 
 class TestLRU(unittest.TestCase):