diff -r a5bd41cae6df Lib/selectors.py
--- a/Lib/selectors.py	Thu Jan 16 18:58:01 2014 +0100
+++ b/Lib/selectors.py	Mon Jan 20 14:54:34 2014 +0100
@@ -8,6 +8,7 @@ This module allows high-level and effici
 from abc import ABCMeta, abstractmethod
 from collections import namedtuple, Mapping
 import functools
+import math
 import select
 import sys
 
@@ -351,7 +352,12 @@ if hasattr(select, 'poll'):
             return key
 
         def select(self, timeout=None):
-            timeout = None if timeout is None else max(int(1000 * timeout), 0)
+            if timeout is None:
+                timeout = None
+            elif timeout < 0:
+                timeout = 0
+            else:
+                timeout = int(math.ceil(timeout * 1000.0))
             ready = []
             try:
                 fd_event_list = self._poll.poll(timeout)
diff -r a5bd41cae6df Lib/test/test_epoll.py
--- a/Lib/test/test_epoll.py	Thu Jan 16 18:58:01 2014 +0100
+++ b/Lib/test/test_epoll.py	Mon Jan 20 14:54:34 2014 +0100
@@ -255,6 +255,17 @@ class TestEPoll(unittest.TestCase):
         self.addCleanup(epoll.close)
         self.assertEqual(os.get_inheritable(epoll.fileno()), False)
 
+    def test_timeout_rounding(self):
+        # epoll_wait() has a resolution of 1 millisecond, check if the timeout
+        # is correctly rounded to the upper bound
+        epoll = select.epoll()
+        self.addCleanup(epoll.close)
+        for timeout in (1e-2, 1e-3, 1e-4):
+            t0 = time.perf_counter()
+            epoll.poll(timeout)
+            dt = time.perf_counter() - t0
+            self.assertGreaterEqual(dt, timeout)
+
 
 def test_main():
     support.run_unittest(TestEPoll)
diff -r a5bd41cae6df Lib/test/test_selectors.py
--- a/Lib/test/test_selectors.py	Thu Jan 16 18:58:01 2014 +0100
+++ b/Lib/test/test_selectors.py	Mon Jan 20 14:54:34 2014 +0100
@@ -5,7 +5,7 @@ import selectors
 import signal
 import socket
 from test import support
-from time import sleep
+from time import sleep, perf_counter
 import unittest
 import unittest.mock
 try:
@@ -363,6 +363,23 @@ class BaseSelectorTestCase(unittest.Test
         self.assertFalse(s.select(2))
         self.assertLess(time() - t, 2.5)
 
+    def test_timeout_rounding(self):
+        # Issue #20311: Timeout must be rounded to upper bound to wait
+        # *at least* timeout seconds. For example, epoll_wait() has a
+        # resolution of 1 ms (10^-3), epoll.select(0.0001) must wait 1 ms,
+        # not 0 ms.
+        s = self.SELECTOR()
+        self.addCleanup(s.close)
+
+        rd, wr = self.make_socketpair()
+        s.register(rd, selectors.EVENT_READ)
+
+        for timeout in (1e-2, 1e-4, 1e-7, 1e-10):
+            t0 = perf_counter()
+            s.select(timeout)
+            dt = perf_counter() - t0
+            self.assertGreaterEqual(dt, timeout)
+
 
 class ScalableSelectorMixIn:
 
diff -r a5bd41cae6df Modules/selectmodule.c
--- a/Modules/selectmodule.c	Thu Jan 16 18:58:01 2014 +0100
+++ b/Modules/selectmodule.c	Mon Jan 20 14:54:34 2014 +0100
@@ -1458,7 +1458,9 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
         return NULL;
     }
     else {
-        timeout = (int)(dtimeout * 1000.0);
+        /* epoll_wait() has a resolution of 1 millisecond, round to the upper
+           bound to wait *at least* dtimeout seconds. */
+        timeout = (int)ceil(dtimeout * 1000.0);
     }
 
     if (maxevents == -1) {