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I got my BB MC when I was a seasonal employee years ago. If your an employee there is an employee program benefit link where you apply and guaranteed approval. Their philosophy is you will promote that card if you had one yourself. The card itself has really no benefit though. yes you collect points for using at BB or wherever but that interest rate is no joke. As far as the card, the Citi may be difficult depending on your score since as others have stated Citi is indeed not as forgiving. One thing is that when you apply you want to also have a BB rewards zone account and apply while logged in. You may have better chances of approval but dont quote me on that. Fingerhut sucks in my opinion but its easy to get credit. I've also had good luck with Syncrony bank branded cards when I was having troubles. Others that gave me credit have been Gap, Macys or any of those shopping store cards. Just be sure to pull your report and review before you apply. Simply having mid-600 scores should not be your only key factor as I am sure you are aware.
Another thing is that if you are currently working with Lexington Law to fix items from the past, I would think that it would be frowned upon to go out applying for more credit while your currently working to fix. As I dont know your circumstances or report, just be cautious and know that it will be 800+ over time not overnight. Best of luck with your process. It has taken me 6 years to get my credit from that. The initial problem was I kept applying for stuff and using credit. Don't go down that road like I did. Be content with your current two cards. Finalize your law process and once cleaned up then you should be good to go. Good job with the zero balance on those other cards. Have you considered just requesting increase on those instead? One thing I have been doing this past month and a half is I stopped using my debit card and putting everything on my Amex and paying off each payday. I get my points, rewards while showing and supporting my income and ability to pay to support CLI. Its working for me currently.