On the contrary, at BOA, Chase and other large banks, it's all about cross-marketing products. It most certainly helps if you have a long-standing checking account, your mortgage is serviced by them and they handle your investments and financial advisory services.

Not only will it get a CC approved, but generally at a lower rate and often with the card Fedexed so you have it the next business day.

All of this presuming 800+ credit score. If you're down in the dumps, banks look only at credit risk and that includes -- but don't believe for a moment that it's based solely on -- credit score.