diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index 5d887ed..70e4787 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -1118,7 +1118,10 @@
         # when a string allocation fails with a MemoryError.
         # This used to crash the interpreter,
         # or leak references when the number was smaller.
-        alloc = lambda: u"a" * (sys.maxsize - 100)
+        charwidth = 4 if sys.maxunicode >= 0x10000 else 2
+        # Note: sys.maxsize is half of the actual max allocation because of
+        # the signedness of Py_ssize_t.
+        alloc = lambda: u"a" * (sys.maxsize // charwidth * 2)
         self.assertRaises(MemoryError, alloc)
         self.assertRaises(MemoryError, alloc)