No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Just Google "credit pulls database" and type in the card you're interested in and you'll see the scores and some profile data of everyone that's reported being approved/denied for the card. If your score falls in line with most of the people that were approved, go for it. If you see denial scores in the vacinity of your score, perhaps it's not in your best interest to apply at this time.
UPDATE: Went to branch today and they approved me for 13,400. My CL on my account says 14,000. Seems like the typical scenario from posts I've seen. Thanks everyone for the comments.