diff -r a6bc96c2b8be Lib/asyncio/base_events.py
--- a/Lib/asyncio/base_events.py	Tue Nov 17 00:19:27 2015 +0000
+++ b/Lib/asyncio/base_events.py	Tue Nov 17 02:54:55 2015 -0700
@@ -70,10 +70,6 @@
         return repr(fd)
 
 
-class _StopError(BaseException):
-    """Raised to stop the event loop."""
-
-
 def _check_resolved_address(sock, address):
     # Ensure that the address is already resolved to avoid the trap of hanging
     # the entire event loop when the address requires doing a DNS lookup.
@@ -118,9 +114,6 @@
                              "got host %r: %s"
                              % (host, err))
 
-def _raise_stop_error(*args):
-    raise _StopError
-
 
 def _run_until_complete_cb(fut):
     exc = fut._exception
@@ -129,7 +122,7 @@
         # Issue #22429: run_forever() already finished, no need to
         # stop it.
         return
-    _raise_stop_error()
+    fut._loop.stop()
 
 
 class Server(events.AbstractServer):
@@ -184,6 +177,7 @@
     def __init__(self):
         self._timer_cancelled_count = 0
         self._closed = False
+        self._stopped = None
         self._ready = collections.deque()
         self._scheduled = []
         self._default_executor = None
@@ -295,13 +289,11 @@
         if self.is_running():
             raise RuntimeError('Event loop is running.')
         self._set_coroutine_wrapper(self._debug)
+        self._stopped = False
         self._thread_id = threading.get_ident()
         try:
-            while True:
-                try:
-                    self._run_once()
-                except _StopError:
-                    break
+            while not self._stopped:
+                self._run_once()
         finally:
             self._thread_id = None
             self._set_coroutine_wrapper(False)
@@ -345,11 +337,10 @@
     def stop(self):
         """Stop running the event loop.
 
-        Every callback scheduled before stop() is called will run. Callbacks
-        scheduled after stop() is called will not run. However, those callbacks
-        will run if run_forever is called again later.
+        Every callback already scheduled will still run.  This simply informs
+        run_forever to stop looping after a complete iteration.
         """
-        self.call_soon(_raise_stop_error)
+        self._stopped = True
 
     def close(self):
         """Close the event loop.
diff -r a6bc96c2b8be Lib/asyncio/test_utils.py
--- a/Lib/asyncio/test_utils.py	Tue Nov 17 00:19:27 2015 +0000
+++ b/Lib/asyncio/test_utils.py	Tue Nov 17 02:54:55 2015 -0700
@@ -70,16 +70,6 @@
         loop.run_until_complete(tasks.sleep(0.001, loop=loop))
 
 
-def run_once(loop):
-    """loop.stop() schedules _raise_stop_error()
-    and run_forever() runs until _raise_stop_error() callback.
-    this wont work if test waits for some IO events, because
-    _raise_stop_error() runs before any of io events callbacks.
-    """
-    loop.stop()
-    loop.run_forever()
-
-
 class SilentWSGIRequestHandler(WSGIRequestHandler):
 
     def get_stderr(self):
diff -r a6bc96c2b8be Lib/test/test_asyncio/test_base_events.py
--- a/Lib/test/test_asyncio/test_base_events.py	Tue Nov 17 00:19:27 2015 +0000
+++ b/Lib/test/test_asyncio/test_base_events.py	Tue Nov 17 02:54:55 2015 -0700
@@ -757,6 +757,36 @@
             pass
         self.assertTrue(func.called)
 
+    def test_single_selecter_event_callback_after_stopping(self):
+        # Python issue #25593: A stopped event loop may cause event callbacks
+        # to run more than once.
+        event_setinel = object()
+        callcount = 0
+        doer = None
+
+        def proc_events(event_list):
+            nonlocal doer
+            if event_setinel in event_list:
+                doer = self.loop.call_soon(do_event)
+
+        def do_event():
+            nonlocal callcount
+            callcount += 1
+            self.loop.call_soon(clear_selector)
+
+        def clear_selector():
+            doer.cancel()
+            self.loop._selector.select.return_value = ()
+
+        self.loop._process_events = proc_events
+        self.loop._selector.select.return_value = (event_setinel,)
+
+        for i in range(1, 3):
+            with self.subTest('Loop %d/2' % i):
+                self.loop.call_soon(self.loop.stop)
+                self.loop.run_forever()
+                self.assertEqual(callcount, 1)
+
 
 class MyProto(asyncio.Protocol):
     done = None