Dallas ? The U.S. airline industry is shrinking to a size not seen since the months after the 2001 terror attacks.

The airlines have been trimming flights for the past two years, matching the falling demand for air travel. Additional capacity cuts are under way at American, the nation’s second-largest carrier, and at No. 3 United.

It could get worse.

Most big airlines depend heavily on a relatively small chunk of passengers who pay the highest fares, “and that’s generally business travelers,” says Robert Mann, an aviation consultant in Port Washington, N.Y. “If business travel doesn’t rebound, we’re going to see further (capacity) cuts.”

Less capacity means consumers will be left with fewer flights to choose from and planes will be crowded. Fewer seats normally means higher fares but that might not happen this time unless the economy begins a true recovery and passenger traffic picks up.

Airlines measure capacity in “seat miles,” the number of miles flown multiplied by the number of seats on the planes. Capacity is crucial in the airline industry in the same way that inventories matter to car dealers and retailers. Too much capacity, and airlines have to cut prices, just as a department store stuck with too many suits and dresses will hold a fire sale. Airlines cut capacity by reducing the number of flights or using smaller planes that carry fewer passengers.

The Air Transport Association, the trade group for big U.S. airlines, estimates that carriers will offer fewer than 12.5 billion seat miles in the U.S. in the fourth quarter. That’s not much more than the low of 12.1 billion late in 2001, when airlines were reeling from the Sept. 11 terror attacks, and it’s down 13 percent from the fourth quarter of 2000.

During the recession, low-fare airlines such as JetBlue, AirTran and Southwest have done better than their bigger rivals. The discounters set the prices on many routes, and the network carriers generally match them.

Even Southwest is shrinking about 6 percent this year, and has announced a slightly scaled-back schedule for early 2010.

Bill Owen, Southwest’s chief scheduler, says the airline has been trimming unprofitable routes, but “If it’s full of full-fare business travelers, we’re not about to cut that flight.”