diff --git a/src/allmydata/test/test_introducer.py b/src/allmydata/test/test_introducer.py
index 7b7e29b96..3d3d9e88f 100644
--- a/src/allmydata/test/test_introducer.py
+++ b/src/allmydata/test/test_introducer.py
@@ -2,11 +2,15 @@
 import os, re, itertools
 from base64 import b32decode
 import json
+from socket import socket, AF_INET
 
 from twisted.trial import unittest
 from twisted.internet import defer, address
 from twisted.python import log
 from twisted.python.filepath import FilePath
+from twisted.python.reflect import requireModule
+from twisted.internet.endpoints import AdoptedStreamServerEndpoint
+from twisted.internet.interfaces import IReactorSocket
 
 from foolscap.api import Tub, Referenceable, fireEventually, flushEventualQueue
 from twisted.application import service
@@ -23,6 +27,8 @@ from allmydata.client import create_client
 from allmydata.util import pollmixin, keyutil, idlib, fileutil, iputil, yamlutil
 import allmydata.test.common_util as testutil
 
+fcntl = requireModule("fcntl")
+
 class LoggingMultiService(service.MultiService):
     def log(self, msg, **kw):
         log.msg(msg, **kw)
@@ -314,6 +320,64 @@ class Server(unittest.TestCase):
 
 NICKNAME = u"n\u00EDickname-%s" # LATIN SMALL LETTER I WITH ACUTE
 
+def foolscapEndpointForPortNumber(portnum):
+    """
+    Create an endpoint that can be passed to ``Tub.listen``.
+
+    :param portnum: Either an integer port number indicating which TCP/IPv4
+        port number the endpoint should bind or ``None`` to automatically
+        allocate such a port number.
+
+    :return: A two-tuple of the integer port number allocated and a
+        Foolscap-compatible endpoint object.
+    """
+    if portnum is None:
+        # Bury this reactor import here to minimize the chances of it having
+        # the effect of installing the default reactor.
+        from twisted.internet import reactor
+        if fcntl is not None and IReactorSocket.providedBy(reactor):
+            # On POSIX we can take this very safe approach of binding the
+            # actual socket to an address.  Once the bind succeeds here, we're
+            # no longer subject to any future EADDRINUSE problems.
+            s = socket()
+            try:
+                s.bind(('', 0))
+                portnum = s.getsockname()[1]
+                s.listen(1)
+                fd = os.dup(s.fileno())
+                flags = fcntl.fcntl(fd, fcntl.F_GETFD)
+                flags = flags | os.O_NONBLOCK | fcntl.FD_CLOEXEC
+                fcntl.fcntl(fd, fcntl.F_SETFD, flags)
+                return (
+                    portnum,
+                    AdoptedStreamServerEndpoint(reactor, fd, AF_INET),
+                )
+            finally:
+                s.close()
+        else:
+            # Get a random port number and fall through.  This is necessary on
+            # Windows where Twisted doesn't offer IReactorSocket.  This
+            # approach is error prone for the reasons described on
+            # https://tahoe-lafs.org/trac/tahoe-lafs/ticket/2787
+            portnum = iputil.allocate_tcp_port()
+    return (portnum, "tcp:%d" % (portnum,))
+
+def listenOnUnused(tub, portnum=None):
+    """
+    Start listening on an unused TCP port number with the given tub.
+
+    :param portnum: Either an integer port number indicating which TCP/IPv4
+        port number the endpoint should bind or ``None`` to automatically
+        allocate such a port number.
+
+    :return: An integer indicating the TCP port number on which the tub is now
+        listening.
+    """
+    portnum, endpoint = foolscapEndpointForPortNumber(portnum)
+    tub.listenOn(endpoint)
+    tub.setLocation("localhost:%d" % (portnum,))
+    return portnum
+
 class SystemTestMixin(ServiceMixin, pollmixin.PollMixin):
 
     def create_tub(self, portnum=None):
@@ -323,11 +387,7 @@ class SystemTestMixin(ServiceMixin, pollmixin.PollMixin):
         #tub.setOption("logRemoteFailures", True)
         tub.setOption("expose-remote-exception-types", False)
         tub.setServiceParent(self.parent)
-        if portnum is None:
-            portnum = iputil.allocate_tcp_port()
-        tub.listenOn("tcp:%d" % portnum)
-        self.central_portnum = portnum
-        tub.setLocation("localhost:%d" % self.central_portnum)
+        self.central_portnum = listenOnUnused(tub, portnum)
 
 class Queue(SystemTestMixin, unittest.TestCase):
     def test_queue_until_connected(self):
@@ -414,10 +474,7 @@ class SystemTest(SystemTestMixin, unittest.TestCase):
             #tub.setOption("logRemoteFailures", True)
             tub.setOption("expose-remote-exception-types", False)
             tub.setServiceParent(self.parent)
-            portnum = iputil.allocate_tcp_port()
-            tub.listenOn("tcp:%d" % portnum)
-            tub.setLocation("localhost:%d" % portnum)
-
+            listenOnUnused(tub)
             log.msg("creating client %d: %s" % (i, tub.getShortTubID()))
             c = IntroducerClient(tub, self.introducer_furl,
                                  NICKNAME % str(i),
@@ -895,10 +952,7 @@ class NonV1Server(SystemTestMixin, unittest.TestCase):
         tub = Tub()
         tub.setOption("expose-remote-exception-types", False)
         tub.setServiceParent(self.parent)
-        portnum = iputil.allocate_tcp_port()
-        tub.listenOn("tcp:%d" % portnum)
-        tub.setLocation("localhost:%d" % portnum)
-
+        listenOnUnused(tub)
         c = IntroducerClient(tub, self.introducer_furl,
                              u"nickname-client", "version", "oldest", {},
                              fakeseq, FilePath(self.mktemp()))