diff --git a/Lib/test/regrtest.py b/Lib/test/regrtest.py
index 26c4d04..4553838 100755
--- a/Lib/test/regrtest.py
+++ b/Lib/test/regrtest.py
@@ -66,7 +66,9 @@
 
 -M runs tests that require an exorbitant amount of memory. These tests
 typically try to ascertain containers keep working when containing more than
-2 bilion objects, and only work on 64-bit systems. The passed-in memlimit,
+2 billion objects, which only works on 64-bit systems. There are also some
+tests that try to exhaust the address space of the process, which only makes
+sense on 32-bit systems with at least 2Gb of memory. The passed-in memlimit,
 which is a string in the form of '2.5Gb', determines howmuch memory the
 tests will limit themselves to (but they may go slightly over.) The number
 shouldn't be more memory than the machine has (including swap memory). You
diff --git a/Lib/test/test_bigaddrspace.py b/Lib/test/test_bigaddrspace.py
new file mode 100644
index 0000000..8c215fe
--- /dev/null
+++ b/Lib/test/test_bigaddrspace.py
@@ -0,0 +1,46 @@
+from test import test_support
+from test.test_support import bigaddrspacetest, MAX_Py_ssize_t
+
+import unittest
+import operator
+import sys
+
+
+class StrTest(unittest.TestCase):
+
+    @bigaddrspacetest
+    def test_concat(self):
+        s1 = 'x' * MAX_Py_ssize_t
+        self.assertRaises(OverflowError, operator.add, s1, '?')
+
+    @bigaddrspacetest
+    def test_optimized_concat(self):
+        x = 'x' * MAX_Py_ssize_t
+        try:
+            x = x + '?'     # this statement uses a fast path in ceval.c
+        except OverflowError:
+            pass
+        else:
+            self.fail("should have raised OverflowError")
+        try:
+            x += '?'        # this statement uses a fast path in ceval.c
+        except OverflowError:
+            pass
+        else:
+            self.fail("should have raised OverflowError")
+        self.assertEquals(len(x), MAX_Py_ssize_t)
+
+    ### the following test is pending a patch
+    #   (http://mail.python.org/pipermail/python-dev/2006-July/067774.html)
+    #@bigaddrspacetest
+    #def test_repeat(self):
+    #    self.assertRaises(OverflowError, operator.mul, 'x', MAX_Py_ssize_t + 1)
+
+
+def test_main():
+    test_support.run_unittest(StrTest)
+
+if __name__ == '__main__':
+    if len(sys.argv) > 1:
+        test_support.set_memlimit(sys.argv[1])
+    test_main()
diff --git a/Lib/test/test_support.py b/Lib/test/test_support.py
index 6532c79..a9d5dab 100644
--- a/Lib/test/test_support.py
+++ b/Lib/test/test_support.py
@@ -314,6 +314,12 @@
 _1G = 1024 * _1M
 _2G = 2 * _1G
 
+# Hack to get at the maximum value an internal index can take.
+class _Dummy:
+    def __getslice__(self, i, j):
+        return j
+MAX_Py_ssize_t = _Dummy()[:]
+
 def set_memlimit(limit):
     import re
     global max_memuse
@@ -328,7 +334,9 @@
     if m is None:
         raise ValueError('Invalid memory limit %r' % (limit,))
     memlimit = int(float(m.group(1)) * sizes[m.group(3).lower()])
-    if memlimit < 2.5*_1G:
+    if memlimit > MAX_Py_ssize_t:
+        memlimit = MAX_Py_ssize_t
+    if memlimit < _2G - 1:
         raise ValueError('Memory limit %r too low to be useful' % (limit,))
     max_memuse = memlimit
 
@@ -371,6 +379,17 @@
         return wrapper
     return decorator
 
+def bigaddrspacetest(f):
+    """Decorator for tests that fill the address space."""
+    def wrapper(self):
+        if max_memuse < MAX_Py_ssize_t:
+            if verbose:
+                sys.stderr.write("Skipping %s because of memory "
+                                 "constraint\n" % (f.__name__,))
+        else:
+            return f(self)
+    return wrapper
+
 #=======================================================================
 # Preliminary PyUNIT integration.