diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 3c909a6a3a5..aed4ac004c9 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -223,8 +223,7 @@ static PyTypeObject PySSLMemoryBIO_Type;
 
 static PyObject *PySSL_SSLwrite(PySSLSocket *self, PyObject *args);
 static PyObject *PySSL_SSLread(PySSLSocket *self, PyObject *args);
-static int check_socket_and_wait_for_timeout(PySocketSockObject *s,
-                                             int writing);
+static int PySSL_select(PySocketSockObject *s, int writing);
 static PyObject *PySSL_peercert(PySSLSocket *self, PyObject *args);
 static PyObject *PySSL_cipher(PySSLSocket *self);
 
@@ -588,15 +587,18 @@ static PyObject *PySSL_SSLdo_handshake(PySSLSocket *self)
         ret = SSL_do_handshake(self->ssl);
         err = SSL_get_error(self->ssl, ret);
         PySSL_END_ALLOW_THREADS
+
         if (PyErr_CheckSignals())
             goto error;
+
         if (err == SSL_ERROR_WANT_READ) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 0);
+            sockstate = PySSL_select(sock, 0);
         } else if (err == SSL_ERROR_WANT_WRITE) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 1);
+            sockstate = PySSL_select(sock, 1);
         } else {
             sockstate = SOCKET_OPERATION_OK;
         }
+
         if (sockstate == SOCKET_HAS_TIMED_OUT) {
             PyErr_SetString(PySocketModule.timeout_error,
                             ERRSTR("The handshake operation timed out"));
@@ -1609,11 +1611,17 @@ static void PySSL_dealloc(PySSLSocket *self)
  */
 
 static int
-check_socket_and_wait_for_timeout(PySocketSockObject *s, int writing)
+PySSL_select(PySocketSockObject *s, int writing)
 {
+    int rc;
+#ifdef HAVE_POLL
+    struct pollfd pollfd;
+    _PyTime_t ms;
+#else
+    int nfds;
     fd_set fds;
     struct timeval tv;
-    int rc;
+#endif
 
     /* Nothing to do unless we're in timeout mode (not non-blocking) */
     if ((s == NULL) || (s->sock_timeout == 0))
@@ -1628,25 +1636,17 @@ check_socket_and_wait_for_timeout(PySocketSockObject *s, int writing)
     /* Prefer poll, if available, since you can poll() any fd
      * which can't be done with select(). */
 #ifdef HAVE_POLL
-    {
-        struct pollfd pollfd;
-        int timeout;
+    pollfd.fd = s->sock_fd;
+    pollfd.events = writing ? POLLOUT : POLLIN;
 
-        pollfd.fd = s->sock_fd;
-        pollfd.events = writing ? POLLOUT : POLLIN;
-
-        /* s->sock_timeout is in seconds, timeout in ms */
-        timeout = (int)_PyTime_AsMilliseconds(s->sock_timeout,
-                                              _PyTime_ROUND_CEILING);
-
-        PySSL_BEGIN_ALLOW_THREADS
-        rc = poll(&pollfd, 1, timeout);
-        PySSL_END_ALLOW_THREADS
-
-        goto normal_return;
-    }
-#endif
+    /* s->sock_timeout is in seconds, timeout in ms */
+    ms = (int)_PyTime_AsMilliseconds(s->sock_timeout, _PyTime_ROUND_CEILING);
+    assert(ms <= INT_MAX);
 
+    PySSL_BEGIN_ALLOW_THREADS
+    rc = poll(&pollfd, 1, (int)ms);
+    PySSL_END_ALLOW_THREADS
+#else
     /* Guard against socket too large for select*/
     if (!_PyIsSelectable_fd(s->sock_fd))
         return SOCKET_TOO_LARGE_FOR_SELECT;
@@ -1656,19 +1656,16 @@ check_socket_and_wait_for_timeout(PySocketSockObject *s, int writing)
     FD_ZERO(&fds);
     FD_SET(s->sock_fd, &fds);
 
-    /* See if the socket is ready */
+    /* Wait until the socket becomes ready */
     PySSL_BEGIN_ALLOW_THREADS
+    nfds = Py_SAFE_DOWNCAST(s->sock_fd+1, SOCKET_T, int);
     if (writing)
-        rc = select(Py_SAFE_DOWNCAST(s->sock_fd+1, SOCKET_T, int),
-                    NULL, &fds, NULL, &tv);
+        rc = select(nfds, NULL, &fds, NULL, &tv);
     else
-        rc = select(Py_SAFE_DOWNCAST(s->sock_fd+1, SOCKET_T, int),
-                    &fds, NULL, NULL, &tv);
+        rc = select(nfds, &fds, NULL, NULL, &tv);
     PySSL_END_ALLOW_THREADS
-
-#ifdef HAVE_POLL
-normal_return:
 #endif
+
     /* Return SOCKET_TIMED_OUT on timeout, SOCKET_OPERATION_OK otherwise
        (when we are able to write or when there's something to read) */
     return rc == 0 ? SOCKET_HAS_TIMED_OUT : SOCKET_OPERATION_OK;
@@ -1710,7 +1707,7 @@ static PyObject *PySSL_SSLwrite(PySSLSocket *self, PyObject *args)
         BIO_set_nbio(SSL_get_wbio(self->ssl), nonblocking);
     }
 
-    sockstate = check_socket_and_wait_for_timeout(sock, 1);
+    sockstate = PySSL_select(sock, 1);
     if (sockstate == SOCKET_HAS_TIMED_OUT) {
         PyErr_SetString(PySocketModule.timeout_error,
                         "The write operation timed out");
@@ -1724,21 +1721,24 @@ static PyObject *PySSL_SSLwrite(PySSLSocket *self, PyObject *args)
                         "Underlying socket too large for select().");
         goto error;
     }
+
     do {
         PySSL_BEGIN_ALLOW_THREADS
         len = SSL_write(self->ssl, buf.buf, (int)buf.len);
         err = SSL_get_error(self->ssl, len);
         PySSL_END_ALLOW_THREADS
-        if (PyErr_CheckSignals()) {
+
+        if (PyErr_CheckSignals())
             goto error;
-        }
+
         if (err == SSL_ERROR_WANT_READ) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 0);
+            sockstate = PySSL_select(sock, 0);
         } else if (err == SSL_ERROR_WANT_WRITE) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 1);
+            sockstate = PySSL_select(sock, 1);
         } else {
             sockstate = SOCKET_OPERATION_OK;
         }
+
         if (sockstate == SOCKET_HAS_TIMED_OUT) {
             PyErr_SetString(PySocketModule.timeout_error,
                             "The write operation timed out");
@@ -1847,21 +1847,23 @@ static PyObject *PySSL_SSLread(PySSLSocket *self, PyObject *args)
         count = SSL_read(self->ssl, mem, len);
         err = SSL_get_error(self->ssl, count);
         PySSL_END_ALLOW_THREADS
+
         if (PyErr_CheckSignals())
             goto error;
+
         if (err == SSL_ERROR_WANT_READ) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 0);
+            sockstate = PySSL_select(sock, 0);
         } else if (err == SSL_ERROR_WANT_WRITE) {
-            sockstate = check_socket_and_wait_for_timeout(sock, 1);
-        } else if ((err == SSL_ERROR_ZERO_RETURN) &&
-                   (SSL_get_shutdown(self->ssl) ==
-                    SSL_RECEIVED_SHUTDOWN))
+            sockstate = PySSL_select(sock, 1);
+        } else if (err == SSL_ERROR_ZERO_RETURN &&
+                   SSL_get_shutdown(self->ssl) == SSL_RECEIVED_SHUTDOWN)
         {
             count = 0;
             goto done;
-        } else {
-            sockstate = SOCKET_OPERATION_OK;
         }
+        else
+            sockstate = SOCKET_OPERATION_OK;
+
         if (sockstate == SOCKET_HAS_TIMED_OUT) {
             PyErr_SetString(PySocketModule.timeout_error,
                             "The read operation timed out");
@@ -1870,6 +1872,7 @@ static PyObject *PySSL_SSLread(PySSLSocket *self, PyObject *args)
             break;
         }
     } while (err == SSL_ERROR_WANT_READ || err == SSL_ERROR_WANT_WRITE);
+
     if (count <= 0) {
         PySSL_SetError(self, count, __FILE__, __LINE__);
         goto error;
@@ -1935,6 +1938,7 @@ static PyObject *PySSL_SSLshutdown(PySSLSocket *self)
             SSL_set_read_ahead(self->ssl, 0);
         err = SSL_shutdown(self->ssl);
         PySSL_END_ALLOW_THREADS
+
         /* If err == 1, a secure shutdown with SSL_shutdown() is complete */
         if (err > 0)
             break;
@@ -1952,11 +1956,12 @@ static PyObject *PySSL_SSLshutdown(PySSLSocket *self)
         /* Possibly retry shutdown until timeout or failure */
         ssl_err = SSL_get_error(self->ssl, err);
         if (ssl_err == SSL_ERROR_WANT_READ)
-            sockstate = check_socket_and_wait_for_timeout(sock, 0);
+            sockstate = PySSL_select(sock, 0);
         else if (ssl_err == SSL_ERROR_WANT_WRITE)
-            sockstate = check_socket_and_wait_for_timeout(sock, 1);
+            sockstate = PySSL_select(sock, 1);
         else
             break;
+
         if (sockstate == SOCKET_HAS_TIMED_OUT) {
             if (ssl_err == SSL_ERROR_WANT_READ)
                 PyErr_SetString(PySocketModule.timeout_error,