diff --git a/Lib/test/test_asyncio/test_sslproto.py b/Lib/test/test_asyncio/test_sslproto.py
index 9b198bfd53074a..4ffbc0fbec6bab 100644
--- a/Lib/test/test_asyncio/test_sslproto.py
+++ b/Lib/test/test_asyncio/test_sslproto.py
@@ -59,9 +59,9 @@ def do_handshake(callback):
             return []
 
         waiter.cancel()
-        self.connection_made(ssl_proto, do_handshake=do_handshake)
 
         with test_utils.disable_logger():
+            self.connection_made(ssl_proto, do_handshake=do_handshake)
             self.loop.run_until_complete(handshake_fut)
 
     def test_eof_received_waiter(self):
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 7c5187348bc4ac..e8ec09efd4ad98 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -2076,7 +2076,11 @@ def coro():
         self.assertFalse(m_log.error.called)
 
         with self.assertRaises(ValueError):
-            self.new_task(self.loop, coro())
+            gen = coro()
+            try:
+                self.new_task(self.loop, gen)
+            finally:
+                gen.close()
 
         self.assertTrue(m_log.error.called)
         message = m_log.error.call_args[0][0]