diff --git a/Doc/c-api/object.rst b/Doc/c-api/object.rst
index d895547..8458fe8 100644
--- a/Doc/c-api/object.rst
+++ b/Doc/c-api/object.rst
@@ -342,6 +342,13 @@
    returned.  This is the equivalent to the Python expression ``len(o)``.
 
 
+.. c:function:: Py_ssize_t PyObject_LengthHint(PyObject *o, Py_ssize_t default)
+
+   Return an estimated length for the object *o*. First trying to return its
+   actual length, then an estimate using ``__length_hint__``, and finally
+   returning the default value. On error ``-1`` is returned. This is the
+   equivalent to the Python expression ``operator.length_hint(o, default)``.
+
 .. c:function:: PyObject* PyObject_GetItem(PyObject *o, PyObject *key)
 
    Return element of *o* corresponding to the object *key* or *NULL* on failure.
diff --git a/Doc/library/operator.rst b/Doc/library/operator.rst
index 3860880..93f33ff 100644
--- a/Doc/library/operator.rst
+++ b/Doc/library/operator.rst
@@ -235,6 +235,12 @@
 
 .. XXX: find a better, readable, example
 
+.. function:: length_hint(obj, default=0)
+
+   Return an estimated length for the object *o*. First trying to return its
+   actual length, then an estimate using ``__length_hint__``, and finally
+   returning the default value.
+
 The :mod:`operator` module also defines tools for generalized attribute and item
 lookups.  These are useful for making fast field extractors as arguments for
 :func:`map`, :func:`sorted`, :meth:`itertools.groupby`, or other functions that
diff --git a/Include/abstract.h b/Include/abstract.h
index 44b5af7..8148675 100644
--- a/Include/abstract.h
+++ b/Include/abstract.h
@@ -403,9 +403,8 @@
      PyAPI_FUNC(Py_ssize_t) PyObject_Length(PyObject *o);
 #define PyObject_Length PyObject_Size
 
-#ifndef Py_LIMITED_API
-     PyAPI_FUNC(Py_ssize_t) _PyObject_LengthHint(PyObject *o, Py_ssize_t);
-#endif
+PyAPI_FUNC(int) _PyObject_HasLen(PyObject *o);
+PyAPI_FUNC(Py_ssize_t) PyObject_LengthHint(PyObject *o, Py_ssize_t);
 
        /*
      Guess the size of object o using len(o) or o.__length_hint__().
diff --git a/Lib/test/test_enumerate.py b/Lib/test/test_enumerate.py
index 2e904cf..c0560fe 100644
--- a/Lib/test/test_enumerate.py
+++ b/Lib/test/test_enumerate.py
@@ -1,4 +1,5 @@
 import unittest
+import operator
 import sys
 import pickle
 
@@ -168,15 +169,13 @@
         x = range(1)
         self.assertEqual(type(reversed(x)), type(iter(x)))
 
-    @support.cpython_only
     def test_len(self):
         # This is an implementation detail, not an interface requirement
-        from test.test_iterlen import len
         for s in ('hello', tuple('hello'), list('hello'), range(5)):
-            self.assertEqual(len(reversed(s)), len(s))
+            self.assertEqual(operator.length_hint(reversed(s)), len(s))
             r = reversed(s)
             list(r)
-            self.assertEqual(len(r), 0)
+            self.assertEqual(operator.length_hint(r), 0)
         class SeqWithWeirdLen:
             called = False
             def __len__(self):
@@ -187,7 +186,7 @@
             def __getitem__(self, index):
                 return index
         r = reversed(SeqWithWeirdLen())
-        self.assertRaises(ZeroDivisionError, len, r)
+        self.assertRaises(ZeroDivisionError, operator.length_hint, r)
 
 
     def test_gc(self):
diff --git a/Lib/test/test_iterlen.py b/Lib/test/test_iterlen.py
index 7469a31..57f7101 100644
--- a/Lib/test/test_iterlen.py
+++ b/Lib/test/test_iterlen.py
@@ -45,31 +45,21 @@
 from test import support
 from itertools import repeat
 from collections import deque
-from builtins import len as _len
+from operator import length_hint
 
 n = 10
 
-def len(obj):
-    try:
-        return _len(obj)
-    except TypeError:
-        try:
-            # note: this is an internal undocumented API,
-            # don't rely on it in your own programs
-            return obj.__length_hint__()
-        except AttributeError:
-            raise TypeError
 
 class TestInvariantWithoutMutations(unittest.TestCase):
 
     def test_invariant(self):
         it = self.it
         for i in reversed(range(1, n+1)):
-            self.assertEqual(len(it), i)
+            self.assertEqual(length_hint(it), i)
             next(it)
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
         self.assertRaises(StopIteration, next, it)
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
 
 class TestTemporarilyImmutable(TestInvariantWithoutMutations):
 
@@ -78,12 +68,12 @@
         # length immutability  during iteration
 
         it = self.it
-        self.assertEqual(len(it), n)
+        self.assertEqual(length_hint(it), n)
         next(it)
-        self.assertEqual(len(it), n-1)
+        self.assertEqual(length_hint(it), n-1)
         self.mutate()
         self.assertRaises(RuntimeError, next, it)
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
 
 ## ------- Concrete Type Tests -------
 
@@ -92,10 +82,6 @@
     def setUp(self):
         self.it = repeat(None, n)
 
-    def test_no_len_for_infinite_repeat(self):
-        # The repeat() object can also be infinite
-        self.assertRaises(TypeError, len, repeat(None))
-
 class TestXrange(TestInvariantWithoutMutations):
 
     def setUp(self):
@@ -167,14 +153,15 @@
         it = iter(d)
         next(it)
         next(it)
-        self.assertEqual(len(it), n-2)
+        self.assertEqual(length_hint(it), n - 2)
         d.append(n)
-        self.assertEqual(len(it), n-1)  # grow with append
+        self.assertEqual(length_hint(it), n - 1)  # grow with append
         d[1:] = []
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
         self.assertEqual(list(it), [])
         d.extend(range(20))
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
+
 
 class TestListReversed(TestInvariantWithoutMutations):
 
@@ -186,32 +173,41 @@
         it = reversed(d)
         next(it)
         next(it)
-        self.assertEqual(len(it), n-2)
+        self.assertEqual(length_hint(it), n - 2)
         d.append(n)
-        self.assertEqual(len(it), n-2)  # ignore append
+        self.assertEqual(length_hint(it), n - 2)  # ignore append
         d[1:] = []
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
         self.assertEqual(list(it), [])  # confirm invariant
         d.extend(range(20))
-        self.assertEqual(len(it), 0)
+        self.assertEqual(length_hint(it), 0)
 
 ## -- Check to make sure exceptions are not suppressed by __length_hint__()
 
 
 class BadLen(object):
-    def __iter__(self): return iter(range(10))
+    def __iter__(self):
+        return iter(range(10))
+
     def __len__(self):
         raise RuntimeError('hello')
 
+
 class BadLengthHint(object):
-    def __iter__(self): return iter(range(10))
+    def __iter__(self):
+        return iter(range(10))
+
     def __length_hint__(self):
         raise RuntimeError('hello')
 
+
 class NoneLengthHint(object):
-    def __iter__(self): return iter(range(10))
+    def __iter__(self):
+        return iter(range(10))
+
     def __length_hint__(self):
-        return None
+        return NotImplemented
+
 
 class TestLengthHintExceptions(unittest.TestCase):
 
diff --git a/Lib/test/test_itertools.py b/Lib/test/test_itertools.py
index 90e85a9..ece7f99 100644
--- a/Lib/test/test_itertools.py
+++ b/Lib/test/test_itertools.py
@@ -1723,9 +1723,8 @@
 class LengthTransparency(unittest.TestCase):
 
     def test_repeat(self):
-        from test.test_iterlen import len
-        self.assertEqual(len(repeat(None, 50)), 50)
-        self.assertRaises(TypeError, len, repeat(None))
+        self.assertEqual(operator.length_hint(repeat(None, 50)), 50)
+        self.assertEqual(operator.length_hint(repeat(None), 12), 12)
 
 class RegressionTests(unittest.TestCase):
 
diff --git a/Lib/test/test_operator.py b/Lib/test/test_operator.py
index fa608b9..b445ee0 100644
--- a/Lib/test/test_operator.py
+++ b/Lib/test/test_operator.py
@@ -410,6 +410,31 @@
         self.assertEqual(operator.__ixor__     (c, 5), "ixor")
         self.assertEqual(operator.__iconcat__  (c, c), "iadd")
 
+    def test_length_hint(self):
+        class X(object):
+            def __init__(self, value):
+                self.value = value
+
+            def __length_hint__(self):
+                if type(self.value) is type:
+                    raise self.value
+                else:
+                    return self.value
+
+        self.assertEqual(operator.length_hint([], 2), 0)
+        self.assertEqual(operator.length_hint(iter([1, 2, 3])), 3)
+
+        self.assertEqual(operator.length_hint(X(2)), 2)
+        self.assertEqual(operator.length_hint(X(NotImplemented), 4), 4)
+        self.assertEqual(operator.length_hint(X(TypeError), 12), 12)
+        with self.assertRaises(TypeError):
+            operator.length_hint(X("abc"))
+        with self.assertRaises(ValueError):
+            operator.length_hint(X(-2))
+        with self.assertRaises(LookupError):
+            operator.length_hint(X(LookupError))
+
+
 def test_main(verbose=None):
     import sys
     test_classes = (
diff --git a/Lib/test/test_set.py b/Lib/test/test_set.py
index 8e9e587..da62723 100644
--- a/Lib/test/test_set.py
+++ b/Lib/test/test_set.py
@@ -848,8 +848,6 @@
         for v in self.set:
             self.assertIn(v, self.values)
         setiter = iter(self.set)
-        # note: __length_hint__ is an internal undocumented API,
-        # don't rely on it in your own programs
         self.assertEqual(setiter.__length_hint__(), len(self.set))
 
     def test_pickling(self):
diff --git a/Modules/operator.c b/Modules/operator.c
index 12fdad5..c5369a5 100644
--- a/Modules/operator.c
+++ b/Modules/operator.c
@@ -208,6 +208,31 @@
     return (result == 0);
 }
 
+PyDoc_STRVAR(length_hint__doc__,
+"length_hint(obj, default=0) -> int\n"
+"Return an estimate of the number of items in obj.\n"
+"This is useful for presizing containers when building from an\n"
+"iterable.\n"
+"\n"
+"If the object supports len(), the result will be\n"
+"exact. Otherwise, it may over- or under-estimate by an\n"
+"arbitrary amount. The result will be an integer >= 0.");
+
+static PyObject *length_hint(PyObject *self, PyObject *args)
+{
+    PyObject *obj;
+    Py_ssize_t defaultvalue = 0, res;
+    if (!PyArg_ParseTuple(args, "O|n:length_hint", &obj, &defaultvalue)) {
+        return NULL;
+    }
+    res = PyObject_LengthHint(obj, defaultvalue);
+    if (res == -1 && PyErr_Occurred()) {
+        return NULL;
+    }
+    return PyLong_FromSsize_t(res);
+}
+
+
 PyDoc_STRVAR(compare_digest__doc__,
 "compare_digest(a, b) -> bool\n"
 "\n"
@@ -366,6 +391,8 @@
 
     {"_compare_digest", (PyCFunction)compare_digest, METH_VARARGS,
      compare_digest__doc__},
+     {"length_hint", (PyCFunction)length_hint, METH_VARARGS,
+     length_hint__doc__},
     {NULL,              NULL}           /* sentinel */
 
 };
diff --git a/Objects/abstract.c b/Objects/abstract.c
index a2737dd..b6fc478 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -64,49 +64,67 @@
 }
 #define PyObject_Length PyObject_Size
 
+int
+_PyObject_HasLen(PyObject *o) {
+    return (Py_TYPE(o)->tp_as_sequence && Py_TYPE(o)->tp_as_sequence->sq_length) ||
+        (Py_TYPE(o)->tp_as_mapping && Py_TYPE(o)->tp_as_mapping->mp_length);
+}
 
 /* The length hint function returns a non-negative value from o.__len__()
-   or o.__length_hint__().  If those methods aren't found or return a negative
-   value, then the defaultvalue is returned.  If one of the calls fails,
-   this function returns -1.
+   or o.__length_hint__().  If those methods aren't found.  If one of the calls
+   fails this function returns -1.
 */
 
 Py_ssize_t
-_PyObject_LengthHint(PyObject *o, Py_ssize_t defaultvalue)
+PyObject_LengthHint(PyObject *o, Py_ssize_t defaultvalue)
 {
     _Py_IDENTIFIER(__length_hint__);
-    PyObject *ro, *hintmeth;
-    Py_ssize_t rv;
-
-    /* try o.__len__() */
-    rv = PyObject_Size(o);
-    if (rv >= 0)
-        return rv;
-    if (PyErr_Occurred()) {
-        if (!PyErr_ExceptionMatches(PyExc_TypeError))
+    Py_ssize_t res = PyObject_Length(o);
+    if (res < 0 && PyErr_Occurred()) {
+        if (!PyErr_ExceptionMatches(PyExc_TypeError)) {
             return -1;
+        }
         PyErr_Clear();
     }
-
-    /* try o.__length_hint__() */
-    hintmeth = _PyObject_LookupSpecial(o, &PyId___length_hint__);
-    if (hintmeth == NULL) {
-        if (PyErr_Occurred())
-            return -1;
-        else
-            return defaultvalue;
+    else {
+        return res;
     }
-    ro = PyObject_CallFunctionObjArgs(hintmeth, NULL);
-    Py_DECREF(hintmeth);
-    if (ro == NULL) {
-        if (!PyErr_ExceptionMatches(PyExc_TypeError))
+    PyObject *hint = _PyObject_LookupSpecial(o, &PyId___length_hint__);
+    if (hint == NULL) {
+        if (PyErr_Occurred()) {
             return -1;
-        PyErr_Clear();
+        }
         return defaultvalue;
     }
-    rv = PyLong_Check(ro) ? PyLong_AsSsize_t(ro) : defaultvalue;
-    Py_DECREF(ro);
-    return rv;
+    PyObject *result = PyObject_CallFunctionObjArgs(hint, NULL);
+    Py_DECREF(hint);
+    if (result == NULL) {
+        if (PyErr_ExceptionMatches(PyExc_TypeError)) {
+            PyErr_Clear();
+            return defaultvalue;
+        }
+        return -1;
+    }
+    else if (result == Py_NotImplemented) {
+        Py_DECREF(result);
+        return defaultvalue;
+    }
+    if (!PyLong_Check(result)) {
+        PyErr_Format(PyExc_TypeError, "Length hint must be an integer, not %s",
+            Py_TYPE(result)->tp_name);
+        Py_DECREF(result);
+        return -1;
+    }
+    defaultvalue = PyLong_AsSsize_t(result);
+    Py_DECREF(result);
+    if (defaultvalue < 0 && PyErr_Occurred()) {
+        return -1;
+    }
+    if (defaultvalue < 0) {
+        PyErr_Format(PyExc_ValueError, "__length_hint__() should return >= 0");
+        return -1;
+    }
+    return defaultvalue;
 }
 
 PyObject *
@@ -1687,7 +1705,7 @@
         return NULL;
 
     /* Guess result size and allocate space. */
-    n = _PyObject_LengthHint(v, 10);
+    n = PyObject_LengthHint(v, 10);
     if (n == -1)
         goto Fail;
     result = PyTuple_New(n);
diff --git a/Objects/bytearrayobject.c b/Objects/bytearrayobject.c
index 2bb3a29..26c76d2 100644
--- a/Objects/bytearrayobject.c
+++ b/Objects/bytearrayobject.c
@@ -2282,7 +2282,7 @@
         return NULL;
 
     /* Try to determine the length of the argument. 32 is arbitrary. */
-    buf_size = _PyObject_LengthHint(arg, 32);
+    buf_size = PyObject_LengthHint(arg, 32);
     if (buf_size == -1) {
         Py_DECREF(it);
         return NULL;
diff --git a/Objects/bytesobject.c b/Objects/bytesobject.c
index bf9259f..25c2326 100644
--- a/Objects/bytesobject.c
+++ b/Objects/bytesobject.c
@@ -2651,7 +2651,7 @@
     }
 
     /* For iterator version, create a string object and resize as needed */
-    size = _PyObject_LengthHint(x, 64);
+    size = PyObject_LengthHint(x, 64);
     if (size == -1 && PyErr_Occurred())
         return NULL;
     /* Allocate an extra byte to prevent PyBytes_FromStringAndSize() from
diff --git a/Objects/iterobject.c b/Objects/iterobject.c
index 3cfbeaf..cf4af5b 100644
--- a/Objects/iterobject.c
+++ b/Objects/iterobject.c
@@ -76,9 +76,14 @@
     Py_ssize_t seqsize, len;
 
     if (it->it_seq) {
-        seqsize = PySequence_Size(it->it_seq);
-        if (seqsize == -1)
-            return NULL;
+        if (_PyObject_HasLen(it->it_seq)) {
+            seqsize = PySequence_Size(it->it_seq);
+            if (seqsize == -1)
+                return NULL;
+        }
+        else {
+            return Py_NotImplemented;
+        }
         len = seqsize - it->it_index;
         if (len >= 0)
             return PyLong_FromSsize_t(len);
diff --git a/Objects/listobject.c b/Objects/listobject.c
index 6e0d094..4cc34b5 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -826,7 +826,7 @@
     iternext = *it->ob_type->tp_iternext;
 
     /* Guess a result list size. */
-    n = _PyObject_LengthHint(b, 8);
+    n = PyObject_LengthHint(b, 8);
     if (n == -1) {
         Py_DECREF(it);
         return NULL;