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Well, closing a card is not exactly a good move as it may hurt your credit score, but it may be worth it if the $450 annually is too much for you.If you fly Delta a lot, it may as well be worth it, you may take advantage of all the bonuses and perks if the value of your rewards outweighs the $550 annual fee.

If the primary purpose of getting the American Express card was earning rewards on Delta, then it is easily achieved by other means. General travel credit cards work great for the frequent flyers. There are a lot of such cards, but Discover it® Miles is probably the most worthy one to recommend. It doesn't have any annual fee and it lets you earn miles on any airline, Delta included.