I signed up for 2 AA personal cards and tried to cancel both cards (2 separate calls, 1 card cancel for each call). For the Amex I was offered a $85 statement credit after making 5 purchases (no min. amount necessary). For the Visa I was offered the $85 credit and 750 bonus miles for each month that I spend $750, with the offer valid for the next 16 billing cycles.

The funny part was I told the second CSR about the deal they gave me on the first card and she told me to make the 5 purchases and then try to cancel. I asked if taking the $85 credit and then canceling my card before the annual fee would hurt my relationship with Citi and she said it wouldn't. I don't know if I believe her, but willing to try it out.