@regehr Once I was at a friend's house and his orange cat, named Dip, had fallen asleep on top of a door, two legs draped down either side.

While I was watching he started losing balance, slowly sliding down one side, looking like he was going to tumble. Partway sliding down he wakes up visibly startled paws scrambling until he rights himself.

As his breathing slowed he relaxed his body, dropped his legs back down both sides, laid his head down on the top of the door, and fell asleep again.