Dear Liz: I have and use three credit cards, two of which offer cash-back rewards. The third has no rewards program, so I would like to get rid of it and replace it with a new card that offers cash back or miles. But I’m afraid if I cancel this card my credit score will take a hit, especially since the card has a big chunk of my overall credit limit. What do you suggest?

Answer: You can ask the issuer for a “product change,” which allows you to swap one card for another without closing your account. Typically, your history with the old card is simply transferred to the new one, as is your credit limit.

The new card must be from the same issuer and you usually won’t qualify for any sign-up bonuses. But you won’t risk damaging your scores by closing one account and applying for another.

Research the issuer’s offerings and know which card you want before you call. This is usually a fairly routine process, but if you encounter any resistance, just mention that your other option is to cancel the card. If you’ve been a good customer, the issuer probably will want to keep your business.

A product change also can be a good idea if you want to switch from a rewards card with a high annual fee to one with a lower fee, or no fee. Any rewards you’ve already earned may not be transferable, so be sure to ask.