Index: Lib/random.py
===================================================================
--- Lib/random.py	(revision 81980)
+++ Lib/random.py	(working copy)
@@ -168,9 +168,12 @@
             raise ValueError("non-integer arg 1 for randrange()")
         if stop is default:
             if istart > 0:
-                if istart >= maxwidth:
+                if istart >= 2**32:
                     return self._randbelow(istart)
-                return int(self.random() * istart)
+                try:
+                    return self._smallrandbelow(istart)
+                except AttributeError:
+                    return int(self.random() * istart)
             raise ValueError("empty range for randrange()")
 
         # stop argument supplied.
Index: Modules/_randommodule.c
===================================================================
--- Modules/_randommodule.c	(revision 81980)
+++ Modules/_randommodule.c	(working copy)
@@ -369,7 +369,36 @@
     return Py_None;
 }
 
+/* Generate an integer uniformly distributed in the range [0, n),
+   for n in the range 0 < n < 2**32. */
+
 static PyObject *
+random__smallrandbelow(RandomObject *self, PyObject *obj_n)
+{
+    unsigned long n, r, rmax;
+
+    n = PyLong_AsUnsignedLong(obj_n);
+    if (n == (unsigned long)-1 && PyErr_Occurred())
+        return NULL;
+    if (n == 0UL || n > 0xFFFFFFFFUL) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "Argument n to _smallrandbelow should "
+                        "satisfy 0 < n < 2**32.");
+        return NULL;
+    }
+
+    /* Generate an integer r, uniformly distributed in the range [0, rmax + 1),
+       where rmax + 1 is the largest multiple of n not exceeding 2**32.  Then
+       r % n is uniformly distributed in the range [0, n).
+    */
+    rmax = 0xFFFFFFFFUL - (0xFFFFFFFFUL - (n - 1UL)) % n;
+    r = genrand_int32(self);
+    while (r > rmax)
+        r = genrand_int32(self);
+    return PyLong_FromUnsignedLong(r % n);
+}
+
+static PyObject *
 random_getrandbits(RandomObject *self, PyObject *args)
 {
     int k, i, bytes;
@@ -443,6 +472,9 @@
     {"getrandbits",     (PyCFunction)random_getrandbits,  METH_VARARGS,
         PyDoc_STR("getrandbits(k) -> x.  Generates a long int with "
                   "k random bits.")},
+    {"_smallrandbelow", (PyCFunction)random__smallrandbelow, METH_O,
+        PyDoc_STR("smallrandbelow(n) -> integer.  Generates an integer "
+                  "in the range [0, n).  Requires 0 < n < 2**32.")},
     {NULL,              NULL}           /* sentinel */
 };