diff --git a/Include/ceval.h b/Include/ceval.h
index e9df8684996e23f..418bd13d6321a68 100644
--- a/Include/ceval.h
+++ b/Include/ceval.h
@@ -124,6 +124,20 @@ PyAPI_FUNC(void) PyEval_ReleaseThread(PyThreadState *tstate);
 #define Py_END_ALLOW_THREADS    PyEval_RestoreThread(_save); \
                  }
 
+
+/* Conditionally release and restore the GIL. */
+#define _Py_BEGIN_ALLOW_THREADS_COND(cond) \
+    { \
+        PyThreadState *_save = NULL; \
+        if (cond) { \
+            _save = PyEval_SaveThread(); \
+        }
+#define _Py_END_ALLOW_THREADS_COND \
+        if (_save != NULL) { \
+            PyEval_RestoreThread(_save); \
+        } \
+    }
+
 /* Masks and values used by FORMAT_VALUE opcode. */
 #define FVC_MASK      0x3
 #define FVC_NONE      0x0
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index b9fb7762e3dacdf..47361466f65a8e0 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -357,7 +357,8 @@ select_select_impl(PyObject *module, PyObject *rlist, PyObject *wlist,
     }
 
     do {
-        Py_BEGIN_ALLOW_THREADS
+        int timeout_is_zero = (tvp != NULL && tvp->tv_sec == 0 && tvp->tv_usec == 0);
+        _Py_BEGIN_ALLOW_THREADS_COND(!timeout_is_zero)
         errno = 0;
         n = select(
             max,
@@ -365,7 +366,7 @@ select_select_impl(PyObject *module, PyObject *rlist, PyObject *wlist,
             omax ? &ofdset : NULL,
             emax ? &efdset : NULL,
             tvp);
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
 
         if (errno != EINTR)
             break;
@@ -698,14 +699,14 @@ select_poll_poll_impl(pollObject *self, PyObject *timeout_obj)
     /* call poll() */
     async_err = 0;
     do {
-        Py_BEGIN_ALLOW_THREADS
+        _Py_BEGIN_ALLOW_THREADS_COND(ms != 0)
         errno = 0;
 #ifdef HAVE_PPOLL
         poll_result = ppoll(self->ufds, self->ufd_len, ts_p, NULL);
 #else
         poll_result = poll(self->ufds, self->ufd_len, (int)ms);
 #endif
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
 
         if (errno != EINTR)
             break;
@@ -1034,10 +1035,10 @@ select_devpoll_poll_impl(devpollObject *self, PyObject *timeout_obj)
 
     do {
         /* call devpoll() */
-        Py_BEGIN_ALLOW_THREADS
+        _Py_BEGIN_ALLOW_THREADS_COND(ms != 0)
         errno = 0;
         poll_result = ioctl(self->fd_devpoll, DP_POLL, &dvp);
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
 
         if (errno != EINTR)
             break;
@@ -1513,17 +1514,13 @@ pyepoll_internal_ctl(int epfd, int op, int fd, unsigned int events)
     case EPOLL_CTL_MOD:
         ev.events = events;
         ev.data.fd = fd;
-        Py_BEGIN_ALLOW_THREADS
         result = epoll_ctl(epfd, op, fd, &ev);
-        Py_END_ALLOW_THREADS
         break;
     case EPOLL_CTL_DEL:
         /* In kernel versions before 2.6.9, the EPOLL_CTL_DEL
          * operation required a non-NULL pointer in event, even
          * though this argument is ignored. */
-        Py_BEGIN_ALLOW_THREADS
         result = epoll_ctl(epfd, op, fd, &ev);
-        Py_END_ALLOW_THREADS
         break;
     default:
         result = -1;
@@ -1673,10 +1670,10 @@ select_epoll_poll_impl(pyEpoll_Object *self, PyObject *timeout_obj,
     }
 
     do {
-        Py_BEGIN_ALLOW_THREADS
+        _Py_BEGIN_ALLOW_THREADS_COND(ms != 0)
         errno = 0;
         nfds = epoll_wait(self->epfd, evs, maxevents, (int)ms);
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
 
         if (errno != EINTR)
             break;
@@ -2429,11 +2426,14 @@ select_kqueue_control_impl(kqueue_queue_Object *self, PyObject *changelist,
     }
 
     do {
-        Py_BEGIN_ALLOW_THREADS
+        int timeout_is_zero = (ptimeoutspec != NULL &&
+                               ptimeoutspec->tv_sec == 0 &&
+                               ptimeoutspec->tv_nsec == 0);
+        _Py_BEGIN_ALLOW_THREADS_COND(!timeout_is_zero)
         errno = 0;
         gotevents = kevent(self->kqfd, chl, nchanges,
                            evl, maxevents, ptimeoutspec);
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
 
         if (errno != EINTR)
             break;
diff --git a/Modules/socketmodule.c b/Modules/socketmodule.c
index 82899572f80255a..915d0b36be900b1 100644
--- a/Modules/socketmodule.c
+++ b/Modules/socketmodule.c
@@ -976,7 +976,7 @@ internal_select(PySocketSockObject *s, int writing, PyTime_t interval,
    When the function is retried, recompute the timeout using a monotonic clock.
 
    sock_call_ex() must be called with the GIL held. The socket function is
-   called with the GIL released. */
+   called with the GIL released if the socket is blocking. */
 static int
 sock_call_ex(PySocketSockObject *s,
              int writing,
@@ -1059,9 +1059,9 @@ sock_call_ex(PySocketSockObject *s,
         /* inner loop to retry sock_func() when sock_func() is interrupted
            by a signal */
         while (1) {
-            Py_BEGIN_ALLOW_THREADS
+            _Py_BEGIN_ALLOW_THREADS_COND(s->sock_timeout)
             res = sock_func(s, data);
-            Py_END_ALLOW_THREADS
+            _Py_END_ALLOW_THREADS_COND
 
             if (res) {
                 /* sock_func() succeeded */
@@ -3655,9 +3655,9 @@ _socket_socket_close_impl(PySocketSockObject *s)
            http://lwn.net/Articles/576478/ and
            http://linux.derkeiler.com/Mailing-Lists/Kernel/2005-09/3000.html
            for more details. */
-        Py_BEGIN_ALLOW_THREADS
+        _Py_BEGIN_ALLOW_THREADS_COND(s->sock_timeout)
         res = SOCKETCLOSE(fd);
-        Py_END_ALLOW_THREADS
+        _Py_END_ALLOW_THREADS_COND
         /* bpo-30319: The peer can already have closed the connection.
            Python ignores ECONNRESET on close(). */
         if (res < 0 && errno != ECONNRESET) {