diff -r eaae4008327d Lib/asyncio/base_events.py
--- a/Lib/asyncio/base_events.py	Tue Feb 04 09:49:14 2014 +0100
+++ b/Lib/asyncio/base_events.py	Tue Feb 04 10:21:46 2014 +0100
@@ -618,6 +618,7 @@ class BaseEventLoop(events.AbstractEvent
                 timeout = deadline
             else:
                 timeout = min(timeout, deadline)
+            timeout += self._granularity
 
         # TODO: Instrumentation only in debug mode?
         if logger.isEnabledFor(logging.INFO):
@@ -638,7 +639,7 @@ class BaseEventLoop(events.AbstractEvent
         self._process_events(event_list)
 
         # Handle 'later' callbacks that are ready.
-        now = self.time() + self._granularity
+        now = self.time()
         while self._scheduled:
             handle = self._scheduled[0]
             if handle._when > now:
diff -r eaae4008327d Lib/selectors.py
--- a/Lib/selectors.py	Tue Feb 04 09:49:14 2014 +0100
+++ b/Lib/selectors.py	Tue Feb 04 10:21:46 2014 +0100
@@ -370,9 +370,7 @@ if hasattr(select, 'poll'):
             elif timeout <= 0:
                 timeout = 0
             else:
-                # poll() has a resolution of 1 millisecond, round away from
-                # zero to wait *at least* timeout seconds.
-                timeout = math.ceil(timeout * 1e3)
+                timeout = timeout * 1e3
             ready = []
             try:
                 fd_event_list = self._poll.poll(timeout)
@@ -432,10 +430,6 @@ if hasattr(select, 'epoll'):
                 timeout = -1
             elif timeout <= 0:
                 timeout = 0
-            else:
-                # epoll_wait() has a resolution of 1 millisecond, round away
-                # from zero to wait *at least* timeout seconds.
-                timeout = math.ceil(timeout * 1e3) * 1e-3
             max_ev = len(self._fd_to_key)
             ready = []
             try:
diff -r eaae4008327d Modules/selectmodule.c
--- a/Modules/selectmodule.c	Tue Feb 04 09:49:14 2014 +0100
+++ b/Modules/selectmodule.c	Tue Feb 04 10:21:46 2014 +0100
@@ -1460,7 +1460,7 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
     else {
         /* epoll_wait() has a resolution of 1 millisecond, round away from zero
            to wait *at least* dtimeout seconds. */
-        timeout = (int)ceil(dtimeout * 1000.0);
+        timeout = (int)(dtimeout * 1000.0);
     }
 
     if (maxevents == -1) {