The number of complaints to the federal government about U.S. airlines increased significantly last year, with some carriers seeing big spikes in complaints, according to the latest federal data.

A total of 12,771 complaints about U.S. airlines were filed with the U.S. Department of Transportation in 2015, up nearly 66 percent from the 7,709 complaints filed the previous year. An even bigger number of complaints was filed about the entire air travel industry, including U.S. and foreign airlines, travel agents, tour operators and others.

The airlines with the highest complaint rates were Spirit and Frontier Airlines, according to data from the U.S. Department of Transportation for 2015.

Spirit and Frontier are ultra low-cost carriers where in-flight sodas and carry-on bags cost extra.

Their style of service might be attractive to travelers on a budget, but others who are accustomed to full-service carriers sometimes come away unhappy about the experience.

"There are people who will find it perfectly acceptable … in exchange for a very low price," said Port Washington, N.Y.-based airline consultant Bob Mann in an interview last year. "There are others who don't really understand what they're buying, get on the airplane and are appalled by it, and never do it again."

American Airlines also had a big increase in its complaint rate, and drew a total of 3,983 complaints to the U.S. Department of Transportation last year, up from 1,792 in 2014.

The airline with the lowest complaint rate was Alaska Airlines, followed by Southwest Airlines. Atlanta-based Delta Air Lines came in at No. 5 out of 13 U.S. airlines ranked.

The biggest category of complaints was flight problems, including cancellations, delays and misconnections. More than 6,400 complaints were filed about flight problems in 2015.

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Credit: Kelly Yamanouchi

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Credit: Kelly Yamanouchi

The second most common category of complaints was baggage, followed by reservations/ticketing/boarding, customer service, fares and refunds.

ajc.com

Credit: Kelly Yamanouchi

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Credit: Kelly Yamanouchi

Other smaller complaint categories include disability, oversales, frequent flier, advertising, discrimination and animals.