And AMEX too. They will happily send you a card you have had before, but not issue any bonus, since it's now "once in a lifetime". However, a number of Chase and AMEX cards have the AF waived the first year. So if you can spare the HP, you can cancel the card when the AF comes due, wait a few weeks and reapply, and avoid the fee. Since you aren't getting a sign up bonus for this, you aren't extending the 24 month timeline either.