Many times, when an annual fee comes due and I cannot negotiate my way out of paying the fee, I cancel the card. Over the last few years, to avoid annual fees, I have canceled my Chase Hyatt credit card, (and Rob’s too) my Chase Marriott Rewards Premier card, my Chase United MileagePlus Explorer card, and my Chase Southwest Airlines Rapid Rewards Premier Card. I have canceled my Citi/AAdvantage Platinum Select World Elite Mastercard. I have also canceled my American Express Premier Rewards Gold card in favor of an American Express Everyday Preferred Card. I did all of this and right after got approved for a Barclaycard Arrival Plus World Elite MasterCard with a very nice credit limit.
Most recently, I canceled both mine and Rob’s American Express Gold Delta SkyMiles Cards and my Chase United MileagePlus Explorer card (for the second time).
However, with all of these cards, the credit limit was small. This is because all of these cards were secured just to get big sign-up bonuses and I either
a. Asked for a small credit limit just to ensure the application would be approved
b. Transferred a minimal amount of existing credit to the new card to ensure the application would be approved.
However, I would definitely give more thought about canceling a card that had a higher credit limit. This is because high credit limits are very helpful in accumulating miles and points.