Southwest ( LUV) became the second airline to say it saw a halt to the steep travel declines that occurred early in the first quarter.

In February, "passenger traffic continued to get worse on a weekly basis," said CEO Gary Kelly, on an earnings conference call. "We have not seen that decline continuing throughout March and then now into April."

Kelly declined to say the tough times are over, however, In fact, Southwest announced it will offer voluntary buyouts to nearly all employees and reaffirmed its commitment to shrink by 5% this year. While trends "seem to have bottomed out in March, I'm certainly not ready to call the bottom yet," Kelly said.

On Thursday, Southwest reported its first quarterly loss, excluding special items, since the first quarter of 1991. Excluding special items, the carrier lost $20 million, or 3 cents a share, missing analyst estimates of a 1-cent loss. In trading Thursday afternoon, Southwest shares were down 59 cents to $7.05, while most carriers showed gains.

Like all carriers, Southwest is seeing a steep decline in business travel, which typically involves close-in bookings. "Every recession this happens: Business travel gets cut (and) it doesn't snap back," Kelly said. "It didn't in '91 and it didn't in 2001." He said revenue per available seat mile will fall in the current quarter, probably more steeply than the 2.9% first-quarter decline.

On Wednesday, AMR ( AMR) also said it was seeing stabilization in bookings. CFO Tom Horton said the carrier's first-quarter loss was less than what it expected a month ago, thanks to "close-in traffic build," which boosted revenue. "It's too early to tell whether that portends a positive trend," he said.

A difference is that American CEO Gerard Arpey indicated he is personally optimistic, while Kelly is less so. In fact, in declaring that business travel will not snap back, Kelly directly contradicted Arpey's view. Arpey said Wednesday that, "If we can get the economy stabilized and improving, companies can turn the travel back on just as quickly as they've turned it off."

The remaining carriers report next week, led by Delta ( DAL) and United ( UAUA) on Tuesday.

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