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Browse credit cards from a variety of issuers to see if there's a better card for you.
Chase, Bank of America (if it offers a single digit APR, no range), AMEX, Citi
Citi, Chase and Cap One are the most reliable, but like you said, even a pre-qual with them can turn to a denial if they see something they don't like with a hard pull.
Generally speaking, if you are offered a hard APR (NOT a range), it's a pretty good offer. If they say something like your APR will be XX.XX%-YY.YY% depending on creditworthiness it's not a good offer.
I concur with Capital One's. I had a prequal for Venture. Decided to CLI my Sony Card instead. 24 hours later, no credit change in reports, my prequal was gone. Just my theory.
I also still have a set APR with AMEX ED prequal as of today. Don't have any AMEX cards, so unsure of that one.
I agree with others here...when the APR shows a range it's typically not as firm as when it's very specific. Now, with that being said, I did get both of my Venture One cards back to back and I never got a prequal on Cap One for them. I just decided to cold app moments after trying the prequal and was approved for both.