United Airlines on Friday said it is installing larger overhead bins to its fleet planes, an effort to end the anxiety-provoking and time-consuming game of musical chairs that often ends with travelers having to check their luggage at the gate.

Passengers often battle for some of the most precious real estate on a plane as they opt to carry on their bags to avoid paying checked luggage fees.

“This is my Mona Lisa,” Toby Enqvist, United’s chief customer officer, said at a company event as he showed a photo of six suitcases neatly stacked in the new bins. By the middle of the next decade, United expects to add the bins to about 80% of its fleet.

American Airlines is also taking delivery of more than 60 new Airbus planes with overhead bins that have 40% more storage space than older models and has added bigger overhead bins to more than 70 Boeing 737-800s.

Delta Air Lines earlier this month started selling a $59-a-year subscription that in addition to eight drink vouchers includes earlier boarding, allowing travelers to claim overhead bin space before lower-paying travelers.

United’s bare-bones basic economy fares have the strictest baggage policy of any U.S. airline: Travelers can’t bring a full-size carry-on bag on board. The airline doesn’t have any immediate plans to change that, Enqvist said.