Sorry, I'm coming later after the review and the commit, but I worry about performances of _run_once() since it's the core of asyncio. Yury proposed to only iterate once on self._scheduled when removing delayed calls, and I have the same concern.

Here is a patch which change _run_once() to only iterate once.

IMO the change is obvious, the current iterates twice and makes the same check twice (check the _cancelled attribute of handles).