diff -r 8ab6b404248c Lib/test/test_itertools.py
--- a/Lib/test/test_itertools.py	Mon Feb 02 10:52:56 2015 -0500
+++ b/Lib/test/test_itertools.py	Mon Feb 02 18:58:47 2015 +0200
@@ -266,7 +266,7 @@ class TestBasicOps(unittest.TestCase):
 
     @support.bigaddrspacetest
     def test_combinations_overflow(self):
-        with self.assertRaises(OverflowError):
+        with self.assertRaises((OverflowError, MemoryError)):
             combinations("AA", 2**29)
 
         # Test implementation detail:  tuple re-use
@@ -353,7 +353,7 @@ class TestBasicOps(unittest.TestCase):
 
     @support.bigaddrspacetest
     def test_combinations_with_replacement_overflow(self):
-        with self.assertRaises(OverflowError):
+        with self.assertRaises((OverflowError, MemoryError)):
             combinations_with_replacement("AA", 2**30)
 
         # Test implementation detail:  tuple re-use
@@ -428,10 +428,8 @@ class TestBasicOps(unittest.TestCase):
 
     @support.bigaddrspacetest
     def test_permutations_overflow(self):
-        with self.assertRaises(OverflowError):
+        with self.assertRaises((OverflowError, MemoryError)):
             permutations("A", 2**30)
-        with self.assertRaises(OverflowError):
-            permutations("A", 2, 2**30)
 
     @support.impl_detail("tuple reuse is specific to CPython")
     def test_permutations_tuple_reuse(self):
@@ -964,8 +962,8 @@ class TestBasicOps(unittest.TestCase):
 
     @support.bigaddrspacetest
     def test_product_overflow(self):
-        with self.assertRaises(OverflowError):
-            product(["a"]*(2**16), repeat=2**16)
+        with self.assertRaises((OverflowError, MemoryError)):
+            product(*(['ab']*2**5), repeat=2**25)
 
     @support.impl_detail("tuple reuse is specific to CPython")
     def test_product_tuple_reuse(self):
diff -r 8ab6b404248c Modules/itertoolsmodule.c
--- a/Modules/itertoolsmodule.c	Mon Feb 02 10:52:56 2015 -0500
+++ b/Modules/itertoolsmodule.c	Mon Feb 02 18:58:47 2015 +0200
@@ -2022,15 +2022,14 @@ product_new(PyTypeObject *type, PyObject
         nargs = 0;
     } else {
         nargs = PyTuple_GET_SIZE(args);
-        if (repeat > PY_SSIZE_T_MAX/sizeof(Py_ssize_t) ||
-            nargs > PY_SSIZE_T_MAX/(repeat * sizeof(Py_ssize_t))) {
+        if ((size_t)nargs > PY_SSIZE_T_MAX/sizeof(Py_ssize_t)/repeat) {
             PyErr_SetString(PyExc_OverflowError, "repeat argument too large");
             return NULL;
         }
     }
     npools = nargs * repeat;
 
-    indices = PyMem_Malloc(npools * sizeof(Py_ssize_t));
+    indices = PyMem_New(Py_ssize_t, npools);
     if (indices == NULL) {
         PyErr_NoMemory();
         goto error;
@@ -2368,11 +2367,7 @@ combinations_new(PyTypeObject *type, PyO
         goto error;
     }
 
-    if (r > PY_SSIZE_T_MAX/sizeof(Py_ssize_t)) {
-        PyErr_SetString(PyExc_OverflowError, "r is too big");
-        goto error;
-    }
-    indices = PyMem_Malloc(r * sizeof(Py_ssize_t));
+    indices = PyMem_New(Py_ssize_t, r);
     if (indices == NULL) {
         PyErr_NoMemory();
         goto error;
@@ -2713,11 +2708,7 @@ cwr_new(PyTypeObject *type, PyObject *ar
         goto error;
     }
 
-    if (r > PY_SSIZE_T_MAX/sizeof(Py_ssize_t)) {
-        PyErr_SetString(PyExc_OverflowError, "r is too big");
-        goto error;
-    }
-    indices = PyMem_Malloc(r * sizeof(Py_ssize_t));
+    indices = PyMem_New(Py_ssize_t, r);
     if (indices == NULL) {
         PyErr_NoMemory();
         goto error;
@@ -3058,13 +3049,8 @@ permutations_new(PyTypeObject *type, PyO
         goto error;
     }
 
-    if (n > PY_SSIZE_T_MAX/sizeof(Py_ssize_t) ||
-        r > PY_SSIZE_T_MAX/sizeof(Py_ssize_t)) {
-        PyErr_SetString(PyExc_OverflowError, "parameters too large");
-        goto error;
-    }
-    indices = PyMem_Malloc(n * sizeof(Py_ssize_t));
-    cycles = PyMem_Malloc(r * sizeof(Py_ssize_t));
+    indices = PyMem_New(Py_ssize_t, n);
+    cycles = PyMem_New(Py_ssize_t, r);
     if (indices == NULL || cycles == NULL) {
         PyErr_NoMemory();
         goto error;