diff --git a/tests/test_async.py b/tests/test_async.py
index dfc7b598..975e7f4d 100755
--- a/tests/test_async.py
+++ b/tests/test_async.py
@@ -504,7 +504,7 @@ class AsyncTests(ConnectingTestCase):
                 raise Exception("Unexpected result from poll: %r", state)
             polls += 1
 
-        self.assert_(polls >= 8, polls)
+        self.assert_(polls >= 5, polls)
 
     def test_poll_noop(self):
         self.conn.poll()
diff --git a/tests/test_green.py b/tests/test_green.py
index e558d626..5e2ae513 100755
--- a/tests/test_green.py
+++ b/tests/test_green.py
@@ -152,7 +152,7 @@ class GreenTestCase(ConnectingTestCase):
             """)
 
         polls = stub.polls.count(POLL_READ)
-        self.assert_(polls > 8, polls)
+        self.assert_(polls > 6, polls)
 
 
 class CallbackErrorTestCase(ConnectingTestCase):