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How long ago was the derog?
Have you tried any prequal tools? Amex for example?
What is your credit score?
What cards do you currently have or have you had in the past (including closed cards), along with dates of when you were approved for the cards? Please include month and year for any card approved in the last 3 years.
Are you targeting points, Companion Passes, hotel or airline statuses, First Class, Biz, Economy seating(s) or cash back?
What point/miles do you currently have?
What is the airport you're flying out of?
Where would you like to go? (The More specific you are, the better someone can recommend the right card. Tokyo is great, "International travel" is way too vague)
Stole the above from reddit but more condensed.
OP, it would be helpful if you provided your FICO scores across all 3 bureaus. You can go to creditchecktotal.com and sign up for the trial and cancel, get your scores/report, and cancel a day later (and still have the benefits for the rest of the week). When you cancel, you are able to get their free plan which is definitely helpful for credit monitoring.
Prequals should not bring your scores down at all. They are soft inq, not hard inq. When applying for the actual account, that is when you see a temporary score "ding". If approved, the account will show available credit, with that your utilization should drop, when the account ages, it helps with average age of accounts. Initially when applying you'll see a small dip. But it should change quickly.