Southwest Airlines, which carries more domestic passengers than any other U.S. airline, will become the latest to stuff more seats into its aircraft so it can sell more tickets on each flight.

Southwest is redoing the interiors of its jets, replacing the seat cushions with thinner foam materials while keeping most of the same frames and swapping out bulky seat-back pockets for mesh. The thinner cushions are actually more comfortable, Southwest says, and even though the airline is adding one more row of seats to its Boeing...