But you're still hurting your credit score.
If you have good credit already, it really doesn't matter that much. If you are a borderline case, I could see it being an issue. In that case you will have to notify the bureaus that you've cancelled the card.
Bingo! Too many people do not understand that. Mine is close to 800. And, because of that, we got a much better mortgage rate when we built our new house two years ago. Then, we pay our mortgage on an automatic (transfer) semi-monthly basis... mortgage will be paid off in 12 years.