diff --git a/Objects/object.c b/Objects/object.c
index 20950c1e8d8..7bf2a634488 100644
--- a/Objects/object.c
+++ b/Objects/object.c
@@ -376,40 +376,28 @@ try_rich_compare_bool(PyObject *v, PyObject *w, int op)
 static int
 try_rich_to_3way_compare(PyObject *v, PyObject *w)
 {
+	static struct { int op; int outcome; } tries[3] = {
+		/* Try this operator, and if it is true, use this outcome: */
+		{Py_EQ, 0},
+		{Py_LT, -1},
+		{Py_GT, 1},
+	};
+	int i;
+
 	if (v->ob_type->tp_richcompare == NULL &&
 	    w->ob_type->tp_richcompare == NULL)
 		return 2; /* Shortcut */
-	switch (try_rich_compare_bool(v, w, Py_LT)) {
-	case -1: /* Error */
-		return -1;
-	case 0: /* False: not less */
-		break;
-	case 1: /* True: less */
-		return -1;
-	case 2: /* NotImplemented */
-		break;
+
+	for (i = 0; i < 3; i++) {
+		switch (try_rich_compare_bool(v, w, tries[i].op)) {
+		case -1:
+			return -1;
+		case 1:
+			return tries[i].outcome;
+		}
 	}
-	switch (try_rich_compare_bool(v, w, Py_GT)) {
-	case -1: /* Error */
-		return -1;
-	case 0: /* False: not greater */
-		break;
-	case 1: /* True: greater */
-		return 1;
-	case 2: /* NotImplemented */
-		break;
-	}
-	switch (try_rich_compare_bool(v, w, Py_EQ)) {
-	case -1: /* Error */
-		return -1;
-	case 0: /* False: not equal */
-		break;
-	case 1: /* True: equal */
-		return 0;
-	case 2: /* NotImplemented */
-		break;
-	}
-	return 2; /* XXX Even if all three returned FALSE?! */
+
+	return 2;
 }
 
 /* Try a 3-way comparison, returning an int.  Return:
@@ -530,9 +518,7 @@ do_cmp(PyObject *v, PyObject *w)
 	return default_3way_compare(v, w);
 }
 
-PyObject *_PyCompareState_Key;
-
-/* _PyCompareState_nesting is incremented before calling compare (for
+/* compare_nesting is incremented before calling compare (for
    some types) and decremented on exit.  If the count exceeds the
    nesting limit, enable code to detect circular data structures.
 */
@@ -541,25 +527,31 @@ PyObject *_PyCompareState_Key;
 #else
 #define NESTING_LIMIT 500
 #endif
-int _PyCompareState_nesting = 0;
+static int compare_nesting = 0;
 
 static PyObject*
 get_inprogress_dict(void)
 {
+	static PyObject *key;
 	PyObject *tstate_dict, *inprogress;
 
+	if (key == NULL) {
+		key = PyString_InternFromString("cmp_state");
+		if (key == NULL)
+			return NULL;
+	}
+
 	tstate_dict = PyThreadState_GetDict();
 	if (tstate_dict == NULL) {
 		PyErr_BadInternalCall();
 		return NULL;
 	} 
-	inprogress = PyDict_GetItem(tstate_dict, _PyCompareState_Key); 
+	inprogress = PyDict_GetItem(tstate_dict, key); 
 	if (inprogress == NULL) {
 		inprogress = PyDict_New();
 		if (inprogress == NULL)
 			return NULL;
-		if (PyDict_SetItem(tstate_dict, _PyCompareState_Key,
-				   inprogress) == -1) {
+		if (PyDict_SetItem(tstate_dict, key, inprogress) == -1) {
 		    Py_DECREF(inprogress);
 		    return NULL;
 		}
@@ -656,8 +648,8 @@ PyObject_Compare(PyObject *v, PyObject *w)
 		return 0;
 	vtp = v->ob_type;
 	wtp = w->ob_type;
-	_PyCompareState_nesting++;
-	if (_PyCompareState_nesting > NESTING_LIMIT &&
+	compare_nesting++;
+	if (compare_nesting > NESTING_LIMIT &&
 		(vtp->tp_as_mapping
 		 || PyInstance_Check(v)
 		 || (vtp->tp_as_sequence && !PyString_Check(v)))) {
@@ -690,7 +682,7 @@ PyObject_Compare(PyObject *v, PyObject *w)
 		result = do_cmp(v, w);
 	}
 exit_cmp:
-	_PyCompareState_nesting--;
+	compare_nesting--;
 	return result < 0 ? -1 : result;
 }
 
@@ -738,30 +730,45 @@ PyObject_RichCompare(PyObject *v, PyObject *w, int op)
 
 	assert(Py_LT <= op && op <= Py_GE);
 
-	if (_PyCompareState_nesting > NESTING_LIMIT) {
-		/* Too deeply nested -- assume equal */
-		/* XXX This is an unfair shortcut!
-		   Should use the same logic as PyObject_Compare. */
-		switch (op) {
-		case Py_LT:
-		case Py_NE:
-		case Py_GT:
-			res = Py_False;
-			break;
-		case Py_LE:
-		case Py_EQ:
-		case Py_GE:
-			res = Py_True;
-			break;
+	compare_nesting++;
+	if (compare_nesting > NESTING_LIMIT &&
+		(v->ob_type->tp_as_mapping
+		 || PyInstance_Check(v)
+		 || (v->ob_type->tp_as_sequence && !PyString_Check(v)))) {
+		/* try to detect circular data structures */
+		PyObject *inprogress, *pair;
+
+		inprogress = get_inprogress_dict();
+		if (inprogress == NULL) {
+                        res = NULL;
+                        goto exit_cmp;
 		}
-		Py_INCREF(res);
-		return res;
+		pair = make_pair(v, w);
+		if (PyDict_GetItem(inprogress, pair)) {
+			/* already comparing these objects.  assume
+			   they're equal until shown otherwise */
+			Py_DECREF(pair);
+			if (op == Py_EQ || op == Py_LE || op == Py_GE)
+				res = Py_True;
+			else
+				res = Py_False;
+			Py_INCREF(res);
+                        goto exit_cmp;
+		}
+		if (PyDict_SetItem(inprogress, pair, pair) == -1) {
+                        res = NULL;
+                        goto exit_cmp;
+		}
+		res = do_richcmp(v, w, op);
+		/* XXX DelItem shouldn't fail */
+		PyDict_DelItem(inprogress, pair);
+		Py_DECREF(pair);
 	}
-
-	_PyCompareState_nesting++;
-	res = do_richcmp(v, w, op);
-	_PyCompareState_nesting--;
-
+	else {
+		res = do_richcmp(v, w, op);
+	}
+  exit_cmp:
+	compare_nesting--;
 	return res;
 }