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DW had a thin file, and i had a derog, but neither of us had both.
Getting approved is a low bar to set. One could get approved but end up with a very low CL and/or very high APR. Why make it more difficult than it needs to be? If you know that you have multiple issues with your credit then work on minizing them and then applying. Always address derogs first. Hit Rebuilding to see what you can do about them.
As always, credit is a marathon, not a sprint. If your last derogs falls off in 5 months then wait and verify that it is off your reports before applying for anything.
I'd wait for the derog to fall off.
However Discover gives credit to people with thin files and not too many accounts, and then grows with them. Unlike say Chase Freedom which is bad with low starting limit and high APRs, Discover will rise eventually.
I started with Discover with no derogs, 7 month old credit file, 2 cards on the report, and approx 670 TU.
They gave me $750. That's March-April 2013.
As of today it's $11,500. I've taken only one CLI with a HP ($750-$2000 in Nov 2013) and the rest are all SP.
My TU now is 740-750.
Since last month I'm enjoying another 12-month 0% APR so that's no bother.
Thin file is not the problem; I'd only wait till the file is clean (no derogs).
i got approved with a 641 Eq and a 610 Ex, i had a few baddies from late student loans..... and i got a $1500 limit. i didnt get the introductory 0% apr for 15 months or any offer. but i was glad to be in.
I also got in with my scores around what they show now. I have a BK7 DC 26 months ago. Great re-build going on and nothing bad since. $800SL just glad to be in.