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What are the dates of the lates?
I think 2 years is the magical time when 30 day lates start to hurt you less. Don't know if that also applies to 60 day lates. The credit card board would have a better feel for what it takes to get a Discover IT or that other card. Discover IT seems to be really hot over there and Discover tends to be more picky in general, though - probably even more so for the IT. Maybe try GWing those lates....