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What are your current scores? Saw on CK that someone got approved with TU 614 EQ 571 EX 654 (dunno how accurate that is)
These types of cards aren't very difficult to get. I got approved for the American Advantage card 5 or 6 years ago with no income! If you have CSP and AmEx you shouldn't have anything to worry about.
You should be fine. The limit might not be the highest, but you should be able to get it.
When I got approved a few years ago my EX score was 680. I had to ask for reconsideration. I think you have ab dry good chance though. Have you tried the Chase pre qualifier?
I was approved 2 years ago after getting a car (so I had auto loan inquiries there, no other injuries). I was not monitoring my scores at that time but the car dealer told me that my score was 679 (or about that, don't remember what CB). I was stunned b/c I had brought a score about a month before and it was 702 and nothing really changed during that time. Anyway, at the time I had 4 store cards all $2k or under in credit each and AMEX w/ $6k limit and capital one w/ $5k limt and very high utilization. I got a pre-approval in the mail (I think b/c of all the auto loan inquiries) and was instantly approved over the phone for $5k.
I applied in October of 2014.
They pulled EX which was in the 780's at the time. Approved for 32k.