Staszak adds that cardholders trying to consolidate should watch their credit limits. Because one-third of your credit score is based on how you keep debt under control, consumers who limit their debt to 30 percent of their credit limit will be rewarded with sweeter scores.

Fortunately, there is a loophole, Gupta says. To give consumers the freedom to shop around for the best rates, credit bureaus provide a 15-day window, starting from the day their first credit score is pulled, when several banks can file credit inquiries while only impacting the score once. Each inquiry made beyond that window will lower the credit score by up to five points, says Gupta, so it's crucial to squeeze rate-shopping into two weeks or less.