If you’re looking for the cheapest day to buy American Airlines tickets, Tuesdays and Wednesdays are great days. They’re not so crowded, so fewer people and thus cheaper fares. American Airlines and all such airlines will be having start-of-the-week specials, and others will have the same by midweek and make hay while sitting in follow-up prices.
Tuesday afternoon is the ideal time to book. That is when the airlines release new fare drops and fares go down. If you want to book lowest one-way American Airlines flights, this is your time.

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