diff --git a/Lib/test/test_class.py b/Lib/test/test_class.py
index 92c220ef6fd..6c91deb129b 100644
--- a/Lib/test/test_class.py
+++ b/Lib/test/test_class.py
@@ -368,3 +368,37 @@ except AttributeError, x:
     pass
 else:
     print "attribute error for I.__init__ got masked"
+
+
+# Test comparison and hash of methods
+class A:
+    def __init__(self, x):
+        self.x = x
+    def f(self):
+        pass
+    def g(self):
+        pass
+    def __eq__(self, other):
+        return self.x == other.x
+    def __hash__(self):
+        return self.x
+class B(A):
+    pass
+
+a1 = A(1)
+a2 = A(2)
+assert a1.f == a1.f
+assert a1.f != a2.f
+assert a1.f != a1.g
+assert a1.f == A(1).f
+assert hash(a1.f) == hash(a1.f)
+assert hash(a1.f) == hash(A(1).f)
+
+assert A.f != a1.f
+assert A.f != A.g
+assert B.f == A.f
+assert hash(B.f) == hash(A.f)
+
+# the following triggers a SystemError in 2.4
+a = A(hash(A.f.im_func)^(-1))
+hash(a.f)
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index 32796bf94d9..ca91042ce67 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -4014,11 +4014,24 @@ def methodwrapper():
 
     l = []
     vereq(l.__add__, l.__add__)
-    verify(l.__add__ != [].__add__)
+    vereq(l.__add__, [].__add__)
+    verify(l.__add__ != [5].__add__)
+    verify(l.__add__ != l.__mul__)
     verify(l.__add__.__name__ == '__add__')
     verify(l.__add__.__self__ is l)
     verify(l.__add__.__objclass__ is list)
     vereq(l.__add__.__doc__, list.__add__.__doc__)
+    try:
+        hash(l.__add__)
+    except TypeError:
+        pass
+    else:
+        raise TestFailed("no TypeError from hash([].__add__)")
+
+    t = ()
+    t += (7,)
+    vereq(t.__add__, (7,).__add__)
+    vereq(hash(t.__add__), hash((7,).__add__))
 
 def notimplemented():
     # all binary methods should be able to return a NotImplemented
diff --git a/Objects/classobject.c b/Objects/classobject.c
index 6d2c648de52..9e57269d24d 100644
--- a/Objects/classobject.c
+++ b/Objects/classobject.c
@@ -2221,9 +2221,17 @@ instancemethod_dealloc(register PyMethodObject *im)
 static int
 instancemethod_compare(PyMethodObject *a, PyMethodObject *b)
 {
-	if (a->im_self != b->im_self)
+	int cmp;
+	cmp = PyObject_Compare(a->im_func, b->im_func);
+	if (cmp)
+		return cmp;
+
+	if (a->im_self == b->im_self)
+		return 0;
+	if (a->im_self == NULL || b->im_self == NULL)
 		return (a->im_self < b->im_self) ? -1 : 1;
-	return PyObject_Compare(a->im_func, b->im_func);
+	else
+		return PyObject_Compare(a->im_self, b->im_self);
 }
 
 static PyObject *
@@ -2299,7 +2307,10 @@ instancemethod_hash(PyMethodObject *a)
 	y = PyObject_Hash(a->im_func);
 	if (y == -1)
 		return -1;
-	return x ^ y;
+	x = x ^ y;
+	if (x == -1)
+		x = -2;
+	return x;
 }
 
 static int
diff --git a/Objects/descrobject.c b/Objects/descrobject.c
index 561ba4a5f01..606ef053049 100644
--- a/Objects/descrobject.c
+++ b/Objects/descrobject.c
@@ -901,16 +901,28 @@ wrapper_dealloc(wrapperobject *wp)
 static int
 wrapper_compare(wrapperobject *a, wrapperobject *b)
 {
-	if (a->descr == b->descr) {
-		if (a->self == b->self)
-			return 0;
-		else
-			return (a->self < b->self) ? -1 : 1;
-	}
+	if (a->descr == b->descr)
+		return PyObject_Compare(a->self, b->self);
 	else
 		return (a->descr < b->descr) ? -1 : 1;
 }
 
+static long
+wrapper_hash(wrapperobject *wp)
+{
+	int x, y;
+	x = _Py_HashPointer(wp->descr);
+	if (x == -1)
+		return -1;
+	y = PyObject_Hash(wp->self);
+	if (y == -1)
+		return -1;
+	x = x ^ y;
+	if (x == -1)
+		x = -2;
+	return x;
+}
+
 static PyObject *
 wrapper_repr(wrapperobject *wp)
 {
@@ -1008,7 +1020,7 @@ static PyTypeObject wrappertype = {
 	0,					/* tp_as_number */
 	0,					/* tp_as_sequence */
 	0,		       			/* tp_as_mapping */
-	0,					/* tp_hash */
+	(hashfunc)wrapper_hash,			/* tp_hash */
 	(ternaryfunc)wrapper_call,		/* tp_call */
 	0,					/* tp_str */
 	PyObject_GenericGetAttr,		/* tp_getattro */