Renes is right. Additionally, I would add: if you don't need the new Amex card right away, cancel the old and wait until you either need the new or see an attractive sign-up bonus on the new. Also, some people say the "recovery specialist" is more likely to give an annual fee waiver or bonus point offer if you cancel when the annual fee is due, but not before. Don't wait too long: Renes said 30 days.