I just applied for both the Citi Visa and Amex cards. I have had both before. I was approved instantly. Cancellations were all about a year ago, so maybe that had something to do with it.
I only hope they don't pull some crap like denying the bonus in a couple of months because I'm a previous card holder. However, this is my third or fourth go around with these cards. and I've always gotten the bonus miles in the past, so I'm optimistic.
By the way, I was given quite large credit limits (>$15K) on each card, so can I assume from that I have a decent credit score?