Hot damn! I never thought I'd see the day! When I jacked my credit up some years ago, the only two things I truly messed up (read: unfixable mistakes) were a BofA Visa and my oldest TL, a Citi MC. Long story short, neither would not work with me and left without options, I let both go. Fast forward to last November, I get a wage garnishment in the mail from Citi's debt collector/attorneys/whatever (wee!). It paid off about two months ago (and never showed on my credit. Do they normally?). Last week, I cold apped for the AAdvantage Platinum Select card and was instantly approved for a $4500 SL WMC. Spending bonus already met. 
A lot of members on here report that Citi will blacklist you for a long time, but at least I can offer the board a new datapoint - if you pay off your outstanding debt with them, you may be given a second chance! I'm glad I was - and I will treat this like solid gold. And by solid gold, I mean PC it to a DC after I get my 40k miles, at which point it will be my primary card.
BofA has been a bit tougher to get back with. I cold apped for the 1-2-3 Visa during my first "my credit is good again!" spree some 8 months back, they countered with a fully secured 1-2-3 that I took a HP to unsecure last month. They will *not* give me a CLI beyond $800 (even with a HP, which only added salt to the wound) despite having many other cards with limits many times that. It is redundant in my card portfolio and would not be worth maintaining if I didn't force myself to keep a positive TL with them, which I will only continue to do until the 1 year mark unless I see a decent CLI.
For those that would like some numbers re: the Citi app - I'm in Chicago. My EX is frozen, they pulled an EQ of 694. Income is 96k.