diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index f29dda70029..4ae5f976a6b 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -4295,6 +4295,9 @@ class TestCloseFds(unittest.TestCase):
 
 class TestIgnoreEINTR(unittest.TestCase):
 
+    # Sending CONN_MAX_SIZE bytes into a multiprocessing pipe must block
+    CONN_MAX_SIZE = max(support.PIPE_MAX_SIZE, support.SOCK_MAX_SIZE)
+
     @classmethod
     def _test_ignore(cls, conn):
         def handler(signum, frame):
@@ -4303,7 +4306,7 @@ class TestIgnoreEINTR(unittest.TestCase):
         conn.send('ready')
         x = conn.recv()
         conn.send(x)
-        conn.send_bytes(b'x' * support.PIPE_MAX_SIZE)
+        conn.send_bytes(b'x' * cls.CONN_MAX_SIZE)
 
     @unittest.skipUnless(hasattr(signal, 'SIGUSR1'), 'requires SIGUSR1')
     def test_ignore(self):
@@ -4322,7 +4325,7 @@ class TestIgnoreEINTR(unittest.TestCase):
             self.assertEqual(conn.recv(), 1234)
             time.sleep(0.1)
             os.kill(p.pid, signal.SIGUSR1)
-            self.assertEqual(conn.recv_bytes(), b'x' * support.PIPE_MAX_SIZE)
+            self.assertEqual(conn.recv_bytes(), b'x' * self.CONN_MAX_SIZE)
             time.sleep(0.1)
             p.join()
         finally: