diff --git a/tornado/test/netutil_test.py b/tornado/test/netutil_test.py
index 00fc6eaf..f9879946 100644
--- a/tornado/test/netutil_test.py
+++ b/tornado/test/netutil_test.py
@@ -184,12 +184,16 @@ class CaresResolverTest(AsyncTestCase, _ResolverTestMixin):
 
 
 # TwistedResolver produces consistent errors in our test cases so we
-# can test the regular and error cases in the same class.
+# could test the regular and error cases in the same class. However,
+# in the error cases it appears that cleanup of socket objects is
+# handled asynchronously and occasionally results in "unclosed socket"
+# warnings if not given time to shut down (and there is no way to
+# explicitly shut it down). This makes the test flaky, so we do not
+# test error cases here.
 @skipIfNoNetwork
 @unittest.skipIf(twisted is None, "twisted module not present")
 @unittest.skipIf(getattr(twisted, '__version__', '0.0') < "12.1", "old version of twisted")
-class TwistedResolverTest(AsyncTestCase, _ResolverTestMixin,
-                          _ResolverErrorTestMixin):
+class TwistedResolverTest(AsyncTestCase, _ResolverTestMixin):
     def setUp(self):
         super(TwistedResolverTest, self).setUp()
         self.resolver = TwistedResolver()