I tried the increase button on my existing BofA card and a recently transfered MBNA card a month ago. I didn't get an instant decision on both. A week later I recieved 5 or 6 individual pieces of mail from BofA. Each was a denial for CLI for 1 of my cards (by 1 I mean all the letters were about only 1 card, no reference to the other card at all). The letters each said the same thing, mentioning account being opened an insufficient amount of time and information from experian. Haven't checked if there is a hard inquiry from these yet.
If there is a hard inquiry I'll be upset because I read the language to indicate that there would be no inquiry. If there are 5 or 6 hard hits on my report I'll be furious. I didn't attempt more than one CLI on each account.

