diff --git a/tornado/test/twisted_test.py b/tornado/test/twisted_test.py
index cff2b998..64709e9c 100644
--- a/tornado/test/twisted_test.py
+++ b/tornado/test/twisted_test.py
@@ -441,8 +441,16 @@ else:
         'twisted.internet.test.test_process.PTYProcessTestsBuilder': [
             'test_systemCallUninterruptedByChildExit',
             ],
-        'twisted.internet.test.test_tcp.TCPClientTestsBuilder': [],
-        'twisted.internet.test.test_tcp.TCPPortTestsBuilder': [],
+        'twisted.internet.test.test_tcp.TCPClientTestsBuilder': [
+            'test_badContext',  # ssl-related; see also SSLClientTestsMixin
+            ],
+        'twisted.internet.test.test_tcp.TCPPortTestsBuilder': [
+            # These use link-local addresses and cause firewall prompts on mac
+            'test_buildProtocolIPv6AddressScopeID',
+            'test_portGetHostOnIPv6ScopeID',
+            'test_serverGetHostOnIPv6ScopeID',
+            'test_serverGetPeerOnIPv6ScopeID',
+            ],
         'twisted.internet.test.test_tcp.TCPConnectionTestsBuilder': [],
         'twisted.internet.test.test_tcp.WriteSequenceTests': [],
         'twisted.internet.test.test_tcp.AbortConnectionTestCase': [],
diff --git a/tox.ini b/tox.ini
index 88c8c375..a13a975e 100644
--- a/tox.ini
+++ b/tox.ini
@@ -36,7 +36,7 @@ deps =
      MySQL-python
      pycurl
      simplejson
-     twisted>=11.1.0
+     twisted>=12.0.0
 
 # py26-full deliberately runs an older version of twisted to ensure
 # we're still compatible with the oldest version we support.
@@ -52,7 +52,7 @@ basepython = python2.7
 deps =
      MySQL-python
      pycurl
-     twisted>=11.1.0
+     twisted>=12.0.0
 
 [testenv:py27-curl]
 # Same as py27-full, but runs the tests with curl_httpclient by default.
@@ -62,7 +62,7 @@ basepython = python2.7
 deps =
      MySQL-python
      pycurl
-     twisted>=11.0.0
+     twisted>=11.1.0
 commands = python -m tornado.test.runtests --httpclient=tornado.curl_httpclient.CurlAsyncHTTPClient {posargs:}
 
 # No pypy-full yet: pycurl doesn't build with pypy, and installing