diff --git a/Lib/selectors.py b/Lib/selectors.py
index a44d5e9..63392f5 100644
--- a/Lib/selectors.py
+++ b/Lib/selectors.py
@@ -8,6 +8,7 @@
 from abc import ABCMeta, abstractmethod
 from collections import namedtuple, Mapping
 import functools
+import math
 import select
 import sys
 
@@ -351,7 +352,12 @@
             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 --git a/Lib/test/test_epoll.py b/Lib/test/test_epoll.py
index 22e9896..094b0f0 100644
--- a/Lib/test/test_epoll.py
+++ b/Lib/test/test_epoll.py
@@ -47,18 +47,6 @@
         self.serverSocket.listen(1)
         self.connections = [self.serverSocket]
 
-    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 tearDown(self):
         for skt in self.connections:
             skt.close()
@@ -266,6 +254,17 @@
         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 --git a/Lib/test/test_selectors.py b/Lib/test/test_selectors.py
index 34edd76..d306aef 100644
--- a/Lib/test/test_selectors.py
+++ b/Lib/test/test_selectors.py
@@ -5,7 +5,7 @@
 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 +363,22 @@
         self.assertFalse(s.select(2))
         self.assertLess(time() - t, 2.5)
 
+    def test_timeout_rounding(self):
+        # Issue #20311: Timeout must be rounded away from zero 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-3, 1e-4):
+            t0 = perf_counter()
+            s.select(timeout)
+            dt = perf_counter() - t0
+            self.assertGreaterEqual(dt, timeout)
+
 
 class ScalableSelectorMixIn: