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But any savvy evaluation of your choices is going to hinge on your credit score and how you use your cards, Hardekopf said.
In today's dicey credit environment, you need a very good credit score to get a new card. And because applying for credit can hurt your score, you don't want to apply randomly. Indeed, several experts now suggest that consumers get their credit scores before shopping.
In some cases, their scores may reveal that they shouldn't shop at all, Detweiler said. They should instead pay off or pay down their credit cards.
"If there's not much chance that you're going to be able to get another card, you might want to get into a nonprofit credit counseling center to see if you could negotiate lower rates with your existing issuers," she said.
That's not necessarily ideal because getting a creditor to accept a negotiated rate is likely to hurt your credit score. But if your score is already too low to apply for a better deal, and if you're struggling to pay, it may be your best option.
The score most commonly used by lenders is called FICO, generated by Fair Isaac Corp. You can access your current score from MyFico.com for $16, but you can also get it free if you sign up for the 30-day free trial offer on the Web site. The downside is that it signs you up for a credit monitoring service that will cost you $90 annually. If you don't cancel within the 30-day period, the freebie turns expensive.