diff --git a/Lib/test/support.py b/Lib/test/support.py
index 2062dd5..897d905 100644
--- a/Lib/test/support.py
+++ b/Lib/test/support.py
@@ -1039,9 +1039,13 @@
     """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__,))
+            if MAX_Py_ssize_t > 2**32:
+                raise unittest.SkipTest(
+                    "not enough memory: try a 32-bit build instead")
+            else:
+                raise unittest.SkipTest(
+                    "not enough memory: %.1fG minimum needed"
+                    % (MAX_Py_ssize_t / (1024 ** 3)))
         else:
             return f(self)
     return wrapper