After talking with mentors and reading on here, the general consensus is always to be open and honest during the process. That is, tell a place you are interviewing that you have an offer. Or if you get an offer see if another place can move things up.
Well, I got an offer from a place I really like. Then an interview offer comes in and they tell me to let them know if I have an offer so that they can move things up. So I do. Well, that completely backfired. They emailed today saying they are yanking me from their short list because of the offer and that they don't think the timing will work.
I guess it is their loss.