However, there is a related question which occurred to me today: if you also have a belt, do you fasten that before or after you do the fly? I don't normally wear a belt, and I've sometimes noticed that I'm "flying low" when I do (presumably because I've deviated from the auto-pilot of my normal routine), which is slightly embarrassing.
So, a poll:
What sequence do you use?
Top button, fly, belt
Top button, belt, fly
Fly, top button, belt
Aargh, I don't know, and now I'll never be able to do my trousers up again!
(There are less than 3P3 fastening options, because I assume that it's nonsensical to do up the belt before the button that's underneath it.)