diff --git a/Doc/reference/datamodel.rst b/Doc/reference/datamodel.rst
index 9fc9f3a3848a4e..5f7aa88ea31110 100644
--- a/Doc/reference/datamodel.rst
+++ b/Doc/reference/datamodel.rst
@@ -2389,10 +2389,8 @@ left undefined.
 
    .. note::
 
-      In order to have a coherent integer type class, when :meth:`__index__` is
-      defined :meth:`__int__` should also be defined, and both should return
-      the same value.
-
+      If :meth:`__index__` is defined and not :meth:`__int__`, :meth:`__int__`
+      automatically defaults to :meth:`__index__`.
 
 .. method:: object.__round__(self, [,ndigits])
             object.__trunc__(self)
diff --git a/Lib/test/test_index.py b/Lib/test/test_index.py
index a2ac32132e2343..72a4a96a881a22 100644
--- a/Lib/test/test_index.py
+++ b/Lib/test/test_index.py
@@ -60,7 +60,7 @@ def test_int_subclass_with_index(self):
         # subclasses.  See issue #17576.
         class MyInt(int):
             def __index__(self):
-                return int(self) + 1
+                return self + 1
 
         my_int = MyInt(7)
         direct_index = my_int.__index__()
@@ -89,6 +89,13 @@ def __index__(self):
         n = operator.index(bad_int)
         self.assertEqual(n, 0)
 
+    def test_int_defaults_to_index(self):
+        class Test:
+            def __index__(self):
+                return 4
+
+        self.assertEqual(int(Test()), 4)
+
 
 class SeqTestCase:
     # This test case isn't run directly. It just defines common tests
diff --git a/Misc/NEWS.d/next/Core and Builtins/2019-05-06-16-00-50.bpo-33039.5YKYPc.rst b/Misc/NEWS.d/next/Core and Builtins/2019-05-06-16-00-50.bpo-33039.5YKYPc.rst
new file mode 100644
index 00000000000000..79d0742afbbb43
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2019-05-06-16-00-50.bpo-33039.5YKYPc.rst	
@@ -0,0 +1,2 @@
+:meth:`__int__` defaults to :meth:`__index__` when only the latter is
+defined. Patch contributed by Rémi Lapeyre.
diff --git a/Objects/typeobject.c b/Objects/typeobject.c
index 37df4d23e4c192..ece9a43756f6fa 100644
--- a/Objects/typeobject.c
+++ b/Objects/typeobject.c
@@ -5393,8 +5393,9 @@ PyType_Ready(PyTypeObject *type)
         }
     }
 
-    /* Hack for tp_hash and __hash__.
-       If after all that, tp_hash is still NULL, and __hash__ is not in
+    /* Set default methods */
+
+    /* If after all that, tp_hash is still NULL, and __hash__ is not in
        tp_dict, set tp_hash to PyObject_HashNotImplemented and
        tp_dict['__hash__'] equal to None.
        This signals that __hash__ is not inherited.
@@ -5435,6 +5436,14 @@ PyType_Ready(PyTypeObject *type)
             goto error;
     }
 
+    /* If __index__ is defined but not __int__, make it default to __index__.
+       Don't touch __float__ and __complex__ as there could be some loss of
+       precision.
+    */
+    if (type->tp_as_number != NULL && type->tp_as_number->nb_int == NULL) {
+        type->tp_as_number->nb_int = type->tp_as_number->nb_index;
+    }
+
     /* All done -- set the ready flag */
     type->tp_flags =
         (type->tp_flags & ~Py_TPFLAGS_READYING) | Py_TPFLAGS_READY;