American Airlines says only a few hundred of its late December flights remain without pilots scheduled to fly the plane.
A spokesman said Thursday that pilots were picking up extra flights and the airline had more on-call pilots in December than during other months. He said American has not canceled any December flights.
The pilots' union had said that more than 15,000 flights lacked a captain, co-pilot or both when a problem was discovered in the company's scheduling system.
Pilots were allowed to take vacation days in the last two weeks of December even if there wasn't another pilot available to operate the flight.
American declined to say how many flights were affected, but it has not disputed the union's figures. The airline has about 15,000 pilots and roughly 200,000 flights scheduled during December.
Spokesman Matt Miller said the number of unassigned flights was continuing to decrease as pilots picked up additional flying assignments.
Miller declined to say how much the scheduling mix-up will cost Fort Worth-based American Airlines Group Inc.
American is the world's largest airline.