Southwest Airlines plans to stop overbooking flights - an industry practice implicated in an ugly incident on a United Airlines flight that has damaged United’s reputation with the flying public.

Last year Southwest bumped 15,000 passengers off flights, more than any other U.S. airline. Carriers say they sometimes sell more tickets than there are seats because often a few passengers don’t show up.

The practice of overbooking flights has come under intense scrutiny since April 9, when a passenger was dragged off an overbooked United Express plane after refusing to give up his seat for a crew member.

Southwest CEO Gary Kelly said Thursday that the airline had been thinking about ending overbooking for “a long time” because of fewer and fewer no-shows. But the issue gained more urgency after the United incident, he said.

Beth Harbin, a Southwest spokeswoman, said Thursday that with better forecasting tools and a new reservations system coming online next month the airline will no longer have a need to overbook flights.

Politicians in Washington and elsewhere have called for a ban on overselling flights. Some critics have said airlines should leave a few seats empty if they think they will be needed by crew members.

JetBlue is currently the only major U.S. airline with a stated policy that bans overbooking. United said Thursday that it plans to reduce overbooking but not eliminate it entirely.

Dallas-based Southwest did not put a time frame on the policy change. And Kelly noted that Southwest may still need to bump people if, for instance, the airline substitutes a smaller plane for the one originally scheduled, which happens occasionally.

Kelly was asked on an earnings conference call if the move could impact Southwest’s results. He said ending overbooking would have a minor impact on revenue but gave no figures.

Chief Financial Officer Tammy Romo said doing away with overbooking would reduce costs - airlines compensate passengers for giving up their seats - which would offset some of the revenue hit.

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