diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index dd0a9d7a862..d7eb69bb8b8 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -4029,7 +4029,7 @@ def handler(signum, frame):
         conn.send('ready')
         x = conn.recv()
         conn.send(x)
-        conn.send_bytes(b'x'*(1024*1024))   # sending 1 MB should block
+        conn.send_bytes(b'x' * test.support.PIPE_MAX_SIZE)
 
     @unittest.skipUnless(hasattr(signal, 'SIGUSR1'), 'requires SIGUSR1')
     def test_ignore(self):
@@ -4048,7 +4048,8 @@ def test_ignore(self):
             self.assertEqual(conn.recv(), 1234)
             time.sleep(0.1)
             os.kill(p.pid, signal.SIGUSR1)
-            self.assertEqual(conn.recv_bytes(), b'x'*(1024*1024))
+            self.assertEqual(conn.recv_bytes(),
+                             b'x' * test.support.PIPE_MAX_SIZE)
             time.sleep(0.1)
             p.join()
         finally: