I gotta ask, did you spend a week sucking your teeth after that, or did you hand it to them and say "hey, you're paying for expertise and we got it to you faster than we estimated"?

The correct way is the send the customer the almost-final version and wait for the bug report. This way you show how quickly you can tackle the problem but don't make the task look too easy.

Yeah, exactly a week. There was no way we could send it immediately, despite the fact it was ethically dubious to hold back.