diff --git a/mitogen/core.py b/mitogen/core.py
index 428965eb..f58eac83 100644
--- a/mitogen/core.py
+++ b/mitogen/core.py
@@ -1019,7 +1019,60 @@ def _unpickle_context(router, context_id, name):
     return router.context_class(router, context_id, name)
 
 
+class Poller(object):
+    def __init__(self):
+        self._rfds = {}
+        self._wfds = {}
+
+    _repr = 'Poller()'
+
+    @property
+    def readers(self):
+        return list(self._rfds.items())
+
+    @property
+    def writers(self):
+        return list(self._wfds.items())
+
+    def __repr__(self):
+        return self._repr
+
+    def close(self):
+        pass
+
+    def start_receive(self, fd, data=None):
+        self._rfds[fd] = data or fd
+
+    def stop_receive(self, fd):
+        self._rfds.pop(fd, None)
+
+    def start_transmit(self, fd, data=None):
+        self._wfds[fd] = data or fd
+
+    def stop_transmit(self, fd):
+        self._wfds.pop(fd, None)
+
+    def poll(self, timeout=None):
+        _vv and IOLOG.debug('%r.poll(%r)', self, timeout)
+        IOLOG.debug('readers = %r', self._rfds)
+        IOLOG.debug('writers = %r', self._wfds)
+        (rfds, wfds, _), _ = io_op(select.select,
+            self._rfds,
+            self._wfds,
+            (), timeout
+        )
+
+        for fd in rfds:
+            _vv and IOLOG.debug('%r: POLLIN for %r', self, fd)
+            yield self._rfds[fd]
+
+        for fd in wfds:
+            _vv and IOLOG.debug('%r: POLLOUT for %r', self, fd)
+            yield self._wfds[fd]
+
+
 class Latch(object):
+    poller_class = Poller
     closed = False
     _waking = 0
     _sockets = []
@@ -1084,10 +1137,15 @@ class Latch(object):
         _vv and IOLOG.debug('%r._get_sleep(timeout=%r, block=%r)',
                             self, timeout, block)
         e = None
+        poller = self.poller_class()
+        poller.start_receive(rsock.fileno())
         try:
-            io_op(select.select, [rsock], [], [], timeout)
-        except Exception:
-            e = sys.exc_info()[1]
+            try:
+                list(poller.poll(timeout))
+            except Exception:
+                e = sys.exc_info()[1]
+        finally:
+            poller.close()
 
         self._lock.acquire()
         try:
@@ -1435,58 +1493,6 @@ class Router(object):
         self.broker.defer(self._async_route, msg)
 
 
-class Poller(object):
-    def __init__(self):
-        self._rfds = {}
-        self._wfds = {}
-
-    _repr = 'Poller()'
-
-    @property
-    def readers(self):
-        return list(self._rfds.items())
-
-    @property
-    def writers(self):
-        return list(self._wfds.items())
-
-    def __repr__(self):
-        return self._repr
-
-    def close(self):
-        pass
-
-    def start_receive(self, fd, data=None):
-        self._rfds[fd] = data or fd
-
-    def stop_receive(self, fd):
-        self._rfds.pop(fd, None)
-
-    def start_transmit(self, fd, data=None):
-        self._wfds[fd] = data or fd
-
-    def stop_transmit(self, fd):
-        self._wfds.pop(fd, None)
-
-    def poll(self, timeout=None):
-        _vv and IOLOG.debug('%r.poll(%r)', self, timeout)
-        IOLOG.debug('readers = %r', self._rfds)
-        IOLOG.debug('writers = %r', self._wfds)
-        (rfds, wfds, _), _ = io_op(select.select,
-            self._rfds,
-            self._wfds,
-            (), timeout
-        )
-
-        for fd in rfds:
-            _vv and IOLOG.debug('%r: POLLIN for %r', self, fd)
-            yield self._rfds[fd]
-
-        for fd in wfds:
-            _vv and IOLOG.debug('%r: POLLOUT for %r', self, fd)
-            yield self._wfds[fd]
-
-
 class Broker(object):
     poller_class = Poller
     _waker = None
diff --git a/mitogen/parent.py b/mitogen/parent.py
index 9e40d17f..3cfff8fb 100644
--- a/mitogen/parent.py
+++ b/mitogen/parent.py
@@ -654,11 +654,17 @@ POLLER_BY_SYSNAME = {
     'FreeBSD': KqueuePoller,
     'Linux': EpollPoller,
 }
+
 PREFERRED_POLLER = POLLER_BY_SYSNAME.get(
     os.uname()[0],
     mitogen.core.Poller,
 )
 
+# For apps that start threads dynamically, it's possible Latch will also get
+# very high-numbered wait fds when there are many connections, and so select()
+# becomes useless there too. So swap in our favourite poller.
+mitogen.core.Latch.poller_class = PREFERRED_POLLER
+
 
 class TtyLogStream(mitogen.core.BasicStream):
     """