Stopover points matter, but transit cities don't.
If your ticketed route is A-B-C,
you can change it to A-C (nonstop) or A-D-C (different transit point) as long as B was just a transit point, and not an actual stopover.
So if you had more than 24 hours in LAX making it a stopover point, you'd have to pay $100 to get rid of it and instead fly SFO-HKG nonstop.
[This message has been edited by benoit (edited 09-12-2003).]