For example, on a ticket bought a day in advance, American charges $428 for a round trip to Chicago, compared to Southwest's $418. But when fees and taxes are added, American's fare of $448.60 is less than Southwest's $453.20 fare. The two carriers charge an identical $536 fare to Fort Lauderdale, Fla., but American's net price is $556.60, 1.3 percent less than Southwest's $563.70.
Mr. Parsons said travelers looking for the cheapest fares may already be out of luck for the high-demand days around Thanksgiving, Christmas and New Year's. However, there seems to be good availability on nonpeak days, he said.
"When it comes to holiday trips, don't expect any mercy from American Airlines or Southwest," he said.
He advised people wanting to travel for spring break to wait until Southwest releases its next schedule. Now it is selling tickets only through March 9, and carriers aren't offering the lowest fares until Southwest does, he said.
For example, American is selling tickets from D/FW to Seattle for $218 for departure on March 2 and a return on March 9, the last date for which Southwest is selling tickets.
But the same trip booked for travel March 10 with a March 17 return flight is selling for $298.
"It would be wise to wait with all your eyes and ears open," Mr. Parsons said.
Mr. Nason, American's vice president of revenue management, said American thinks customers will pay a little more for a nonstop flight on American rather than a one-stop service or connecting service on Southwest.
For example, American's nonstop service to Los Angeles has an average flight time of 3 hours and 13 minutes, compared with 5 hours and 16 minutes for Southwest.
"Each passenger will have their different valuation -- which airport is more convenient, which airline they like better, how important the nonstop vs. the one-stop is for them," he said. "We think they'll like our value proposition."
Southwest's Mr. Michalenko said American will "do what they have to from a competitive standpoint."
"Southwest by nature is a low-cost, low-fare carrier," Mr. Michalenko said. "That's what we do every day. We don't have to adjust to another carrier, which is what American has to do because they're by nature a higher-cost, higher-fare carrier."
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