diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index 4c5da2fccda..c4810a5ce17 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -651,13 +651,17 @@ class _TestProcess(BaseTestCase):
         from multiprocessing.forkserver import _forkserver
         _forkserver.ensure_running()
 
+        # First process sleeps 500 ms
+        delay = 0.5
+
         evt = self.Event()
-        proc = self.Process(target=self._sleep_and_set_event, args=(evt, 1.0))
+        proc = self.Process(target=self._sleep_and_set_event, args=(evt, delay))
         proc.start()
 
         pid = _forkserver._forkserver_pid
         os.kill(pid, signum)
-        time.sleep(1.0)  # give it time to die
+        # give time to the fork server to die and time to proc to complete
+        time.sleep(delay * 2.0)
 
         evt2 = self.Event()
         proc2 = self.Process(target=self._sleep_and_set_event, args=(evt2,))