After a Kentucky doctor was dragged off a United Airlines plane in April, the nation's airlines vowed to reduce the number of passengers who are bumped from overbooked flights. They seem to be making good on the promise.

After a Kentucky doctor was dragged off a United Airlines plane in April, the nation's airlines vowed to reduce the number of passengers who are bumped from overbooked flights.

They seem to be making good on the promise.

In the July-to-September quarter, the nation's 12 biggest airlines reported the lowest rate of passengers denied seats since the Department of Transportation began tracking the data in 1995.

For the three-month period, the airlines involuntarily denied boarding to 2,745 passengers out of more than 177 million fliers, according to the Transportation Department's Aviation Consumer Protection Division. That's a rate of 15 passengers bumped for every one million fliers.

For the same quarter a year earlier, the bumping rate was 69 for every million fliers. The previous lowest quarterly rate of 44 came in the second quarter of 2017.

United ranked fourth with 4 bumped passengers for every million fliers, below Delta and Virgin America (both at 1) and JetBlue (2), according to the Department of Transportation.

"Today's report reflects what we know to be true — U.S. airlines are improving on the things that matter most to customers when they fly," said Alison McAfee, a spokeswoman for Airlines for America, the trade group for the nation's airlines.

Bumping rates became a hot topic after airport police boarded a fully booked United flight in Chicago on April 9 to remove David Dao, a physician who refused to give up his seat to make room for a flight crew member who needed to fly to Kentucky to work the next day.

Officers ended up physically dragging Dao from the plane. He suffered a concussion, a broken nose and other injuries in the episode. Video of the incident, captured by fellow fliers, went viral.

In response, United and other carriers promised to reduce the number of passengers involuntarily bumped from oversold flights. United said it would offer passengers up to $10,000 to voluntarily give up a seat on an overbooked flight, among other policy changes.

Southwest Airlines — the nation's largest domestic carrier — quickly followed by announcing that it would no longer overbook flights. And JetBlue pointed out during the uproar that it has never overbooked.

Still, Southwest bumped 38 passengers per million fliers in the latest quarter, ranking 10th, just ahead of Frontier at 39. Spirit bumped the most passengers, 54.

Federal regulators allow airlines to oversell their flights because carriers know that there are almost always a few no-shows. Carriers can increase revenues by selling those empty seats at a premium to last-minute fliers.

But when airlines miscalculate, they may bump passengers who do not voluntarily give up their seat, in exchange for cash or a seat on another flight.