For each of the big three U.S. carriers, Latin America was the world's best-performing region in the third quarter of 2016 and the only region that produced positive revenue per available seat mile.

American Airlines (AAL) - Get Report benefited disproportionately.

During the quarter, Delta (DAL) - Get Report  generated 6.3% or $571 million of its passenger revenue in Latin America, where it reported 1.4% RASM growth. United (UAL) - Get Report generated 7.5% or $648 million of its total passenger revenue in Latin America, where it reported a 1.3% RASM decline, its best performance for any sector.

American, meanwhile, derived 11.2% or $1.03 billion of its total passenger revenue from Latin America, where its RASM gain was 1.8%.

Of the three carriers, American also produced the best overall third-quarter RASM performance, a 2.2% decline. United's overall RASM declined 5.8%, while Delta's declined 6.8%.

Looking ahead,"American is likely to be the PRASM/RASM leader among the Big 3 (as well as most other carriers) over the next 9 - 12 months, getting to positive unit revenues before everyone else," Deutsche Bank analyst Mike Linenberg wrote Friday in a report.

During the third quarter, the big three carriers each reported RASM results for four regions: Atlantic, Pacific, Latin America and domestic. Among them, American and Delta's Latin America results showed the only gains.

In the past year, American cut capacity in Latin America, while Delta cut by 3.2% and United added 1.6%.

On American's third-quarter earnings call, President Robert Isom said the improvement in Latin America was "driven by 25% year-over-year improvement in Brazil PRASM as capacity rationalized and the real strengthened," and by continued strength in Mexico.

Looking ahead, Don Casey, senior vice president of revenue management, added, "Brazil is a big factor obviously in the overall result and we're expecting our performance in Brazil in the fourth quarter to be better materially better than the performance in the third quarter."

Commentary on the other third-quarter calls was similar.

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"We expect Latin America to be the first region to return to positive year-over-year PRASM, driven by good results across the region but particularly strong results in Brazil," said United President Scott Kirby. "As we look out to the fourth quarter, at least we expect yields to be somewhere between 20% and 30% {year over year}.

"The pricing environment to Brazil is far, far better than it was just a few months ago," Kirby said. "And that happened sort of around the time that you're going to Olympics and maybe that's what caused it but it stuck. So, Brazil is much improved."

Delta President Glen Hauenstein said the third quarter marked "the first time the Latin entity has achieved a positive unit revenue in 2 1/2 years. After 16 consecutive quarters of negative results, Brazil unit revenue improved 30% year on year, with momentum building through the quarter as the strengthening real drove more Brazil point-of-sale demand."

Hauenstein added that "Mexico business markets have also been a key driver on Latin's path to positive RASM, achieving the third consecutive quarter of positive unit revenues."

One weak spot in the region is Cuba, where six U.S. carriers have or will add service in the next few months as President Obama has moved to normalize relations between the two countries. It will take time to build traffic, the carriers have said.

"I think everyone is struggling a little bit in terms of selling in Cuba," Casey said on the American call. "There are a lot of restrictions that are still in place that made it difficult to sell."

Added CEO Doug Parker, "We're in for the long haul. It's not something we didn't expect.

"This is really a new market and so at any rate we're excited to be the largest carrier there," Parker said. "We're committed to Cuba and making it work and we'll work through the startup to get into the point where eventually where we all expect we'll be."

American's presence in Latin American dates to 1990, when the carrier purchased a Miami-based Latin American route system from Eastern Airlines for $349 million, one of the most successful airline asset purchase deals ever.

"We were expanding internally, buying airplanes, and hiring people, and we needed places to fly the planes," then CEO-Bob Crandall said in an interview for the book, American Airlines, US Airways and the Creation of the World's Largest Airline, which I wrote with Dan Reed.

"Eastern had neglected its Latin American assets," Crandall said. "We were ambivalent about buying it, but (American executive) Peter Dolara said he could fix Latin America. So we bought the assets from Eastern and Peter did fix Latin America."

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.