Delta Air Lines ranked fourth among U.S. airlines in an annual airline study, while AirTran Airways fell to 10th place out of 15 airlines.

The top three spots in the Airline Quality Rating study of airline performance in 2013 were filled by smaller carriers, with Virgin America taking the top spot, followed by JetBlue and Hawaiian Airlines.

Atlanta-based Delta had declines in its performance in baggage handling, on-time results and bumped passengers in 2013 versus 2012, but was still the top-ranked major network carrier in the study released Monday.

Delta acquired Northwest Airlines in 2008 and saw its on-time performance and customer service rankings plummet in the two years following, but then staged a recovery.

The airline put in place a team to analyze complaints for opportunities to improve, started using social media to respond to customers’ problems and invested in better baggage handling systems at hubs in Atlanta and New York, said Delta spokesman Morgan Durrant.

Durrant said Delta has also focused on reducing cancellations by moves like adding maintenance stations and parts at more airports, because avoiding cancellations can prevent other problems like additional delays, lost bags, bumped passengers and complaints.

Meanwhile, AirTran’s ranking dropped from No. 3 to No. 10 in the Airline Quality Rating. That was the biggest drop among all of the carriers studied.

AirTran is in the middle of being folded into Southwest Airlines, with the AirTran name set to disappear by the end of this year. Southwest also saw a decline in its performance while maintaining a No. 8 ranking.

At merging airlines, “that state of transition or uncertainty almost always creates turmoil,” said Dean Headley, associate professor of marketing at Wichita State University and co-author of the study. Then, a few years later, “things tend to kind of pick up.”

Overall, U.S. airlines did worse in on-time performance and baggage handling, but were able to reduce the number of customer complaints to the U.S. Department of Transportation and passengers involuntarily bumped from flights.

With more delays and lost bags — along with the feeling that it costs more to fly as fares rise— “I would think the perception of the consumer is, ‘Hey, it’s really getting worse,’” Headley said. But more travelers are turning to social media to complain and going directly to the airline for remedies, he said, which may explain the decline in customer complaints to the federal government.

This year so far has shown that airlines and their passengers are still at the mercy of the weather. Delta, Southwest and AirTran have struggled with massive cancellations amid two Atlanta ice storms and bad weather in other parts of the country in early 2014.

Delta, for example, canceled 17,000 flights in the first three months of the year due to severe weather, reducing its quarterly profit by $55 million.

Southwest chief operating officer Mike Van De Ven earlier this year apologized to employees for the “magnitude of operational challenges” employees faced during storms in January.

“Our performance was just unacceptable,” Van De Ven said. He said the airline in 2013 revamped its flight schedules. “In hindsight,” he said, those changes caused some delays and other problems — “and that was occurring even when the weather was good.” Bad weather exacerbated the challenges, Van De Ven said.