diff -r 1b2134a78c17 Lib/test/test_int.py
--- a/Lib/test/test_int.py	Fri Dec 28 10:09:54 2012 +0200
+++ b/Lib/test/test_int.py	Fri Dec 28 10:24:43 2012 +0000
@@ -260,6 +260,23 @@
         with self.assertRaises(TypeError):
             int('0', 5.0)
 
+    def test_int_base_indexable(self):
+        class MyIndexable(object):
+            def __init__(self, value):
+                self.value = value
+            def __index__(self):
+                return self.value
+
+        # Check out of range bases.
+        for base in 2**100, -2**100, 1, 37:
+            with self.assertRaises(ValueError):
+                int('43', base)
+
+        # Check in-range bases.
+        self.assertEqual(int('101', base=MyIndexable(2)), 5)
+        self.assertEqual(int('101', base=MyIndexable(10)), 101)
+        self.assertEqual(int('101', base=MyIndexable(36)), 1 + 36**2)
+
     def test_non_numeric_input_types(self):
         # Test possible non-numeric types for the argument x, including
         # subclasses of the explicitly documented accepted types.
diff -r 1b2134a78c17 Objects/longobject.c
--- a/Objects/longobject.c	Fri Dec 28 10:09:54 2012 +0200
+++ b/Objects/longobject.c	Fri Dec 28 10:24:43 2012 +0000
@@ -4265,11 +4265,6 @@
     }
     if (obase == NULL)
         return PyNumber_Long(x);
-    if (!PyLong_Check(obase)) {
-        PyErr_SetString(PyExc_TypeError,
-                        "int() base must be an integer.");
-        return NULL;
-    }
 
     base = PyNumber_AsSsize_t(obase, NULL);
     if (base == -1 && PyErr_Occurred())