NEW YORK (CNNMoney.com) - Southwest Airlines has struck an agreement with its pilots union to have each of them fly an additional 1.5 hours a month, according to a published report.

The Dallas Morning News reported the agreement, which it said will give the nation's most profitable airline even greater cost advantage over the money-losing larger carriers.

The paper said the deal with the Southwest Airlines Pilots' Association will save Southwest roughly $4 million annually because the discounter won't need to hire as many pilots as it expands its schedule about 10 percent a year.

Carl Kuwitzky, a vice president for the union, told the paper that his group has been improving its partnership with Southwest.

"Our pilots have no problem working hard," he said.

Southwest spokesman Ed Stewart acknowledged the agreement, which has not been publicly announced, but he declined to comment further because the carrier typically doesn't discuss its labor relations.

According to the paper, Southwest pilots had about 67 hours of actual flying time a month before the latest agreement, which was reached Nov. 6. The pilots at American Airlines, the industry's largest carrier, have an average in the mid-40-hour range a month, the Morning News said.

Although Southwest has been the most profitable airline, its labor costs are a concern among Wall Street analysts. It is the most heavily unionized carrier among the low-cost, low-fare carriers who have been gaining market share, and the paper reports it spends the most on its employees by most measures.

Much of its profitability has come from the ability to buy fuel more cheaply through long-term fuel contracts. But as fuel prices continue to remain near historically high levels, that cost advantage is likely to lessen.

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