diff --git a/tornado/locks.py b/tornado/locks.py
index 44222a43..94adb322 100644
--- a/tornado/locks.py
+++ b/tornado/locks.py
@@ -15,6 +15,7 @@
 from __future__ import absolute_import, division, print_function
 
 import collections
+from concurrent.futures import CancelledError
 
 from tornado import gen, ioloop
 from tornado.concurrent import Future, future_set_result_unless_cancelled
@@ -196,7 +197,8 @@ class Event(object):
         Done
     """
     def __init__(self):
-        self._future = Future()
+        self._value = False
+        self._waiters = set()
 
     def __repr__(self):
         return '<%s %s>' % (
@@ -204,23 +206,26 @@ class Event(object):
 
     def is_set(self):
         """Return ``True`` if the internal flag is true."""
-        return self._future.done()
+        return self._value
 
     def set(self):
         """Set the internal flag to ``True``. All waiters are awakened.
 
         Calling `.wait` once the flag is set will not block.
         """
-        if not self._future.done():
-            self._future.set_result(None)
+        if not self._value:
+            self._value = True
+
+            for fut in self._waiters:
+                if not fut.done():
+                    fut.set_result(None)
 
     def clear(self):
         """Reset the internal flag to ``False``.
 
         Calls to `.wait` will block until `.set` is called.
         """
-        if self._future.done():
-            self._future = Future()
+        self._value = False
 
     def wait(self, timeout=None):
         """Block until the internal flag is true.
@@ -228,10 +233,21 @@ class Event(object):
         Returns a Future, which raises `tornado.util.TimeoutError` after a
         timeout.
         """
+        fut = Future()
+        if self._value:
+            fut.set_result(None)
+            return fut
+        self._waiters.add(fut)
+        fut.add_done_callback(lambda fut: self._waiters.remove(fut))
         if timeout is None:
-            return self._future
+            return fut
         else:
-            return gen.with_timeout(timeout, self._future)
+            timeout_fut = gen.with_timeout(timeout, fut, quiet_exceptions=(CancelledError,))
+            # This is a slightly clumsy workaround for the fact that
+            # gen.with_timeout doesn't cancel its futures. Cancelling
+            # fut will remove it from the waiters list.
+            timeout_fut.add_done_callback(lambda tf: fut.cancel() if not fut.done() else None)
+            return timeout_fut
 
 
 class _ReleasingContextManager(object):