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Do you mind sharing just how bad the "baddies" are? Sounds like you've found yourself a sympathetic CSR at Chase, I hope you have the same luck when you call back or reapply.
I was instantly approved for the Chase united Explorer Card 10k limit....my score was about 674 on equifax at the time. They pulled experian which has 3 baddies on it, two pretty old and one from an old debt I guess that's been resold and reported newly in 2011. My highest credit limit at the time was probably 1900 on a store card....and 1200 on a prime card (discover). I do have a high income.....hopefully this helps!