European beaches and cities are jam-packed with U.S. tourists eager to venture across the Atlantic now that there are no COVID-19 restrictions to hold them back. But back at home, the air travel recovery appears tapped out.

Alaska Air Group recently forecast weaker-than-expected sales growth for the third quarter. Chief Financial Officer Shane Tackett told Bloomberg News that travelers’ prioritization of international sojourns is coming at the expense of its primarily domestic routes and is weighing on fares. Meanwhile, Southwest Airlines in June ran a promotion for 40% off fares on trips between Aug. 15 and Dec. 14, with the week of Thanksgiving blacked out. Frontier Airlines last week had a sale for $29 fares on select days of the week through Nov. 15. Spirit Airlines offered one-way flights for $50 from Aug. 9 through Oct. 4 excluding Friday and Sunday bookings.

Airlines typically run sales when they’re trying to stimulate demand for weaker booking periods, so these promotions don’t bode well for the fall. For the better part of the last 18 months, airlines have had more demand than the country’s aviation infrastructure could handle. There are still logjams in the airplane manufacturing supply chain that are keeping carriers from taking delivery of the jets they’ve ordered, and other structural capacity constraints, particularly at the busiest airports, are limiting the number of flights they can operate daily. But that balance may be shifting.