American Airlines, which excels at not much of anything, just banked $1.2 billion in profit during its most profitable three months in history. The nation’s other major airlines are also swimming in record profits, largely thanks to fuel prices that plunged 40 percent within a year.

But for Americans booking their summer travel, plane ticket prices are looking just as high as always. Domestic flights booked for between Memorial Day and Labor Day have averaged about $453.87, down a whopping $2.01 since last year, airline data show. (Buy 15 tickets, and you’ll have saved enough to buy this SkyMall cat fun tunnel.)

U.S. airlines spend more on fuel than anything else, guzzling more than 40 million gallons a day, so you can imagine how much historically cheap oil contributes to their bottom line. American, Delta, Southwest and United saved about $3.3 billion on fuel in the first quarter, financial filings show.

But their average fares have barely budged, highlighting once again just how much control airlines have over their paying customers, and how little they worry about competition. The average domestic flight last year cost $391, the highest since federal statisticians started tracking fares in 1995. Adjusted for inflation, fares are at a 12-year high.

Airlines’ record profits are all the more staggering because the first three months of the year — after the holidays but before spring and summer trips — are generally regarded as a cash dead zone. U.S. airlines lost money in every first quarter except one between 2000 and 2013, federal data show.

Just how long the cheap-fuel days will last is anyone’s guess. But summer is airlines’ golden season, and several carriers said they plan to bump up the number of tickets they’ll sell by running more flights or flying bigger jets. Airfare forecaster Hopper expects peak airfares this June will be about $17 cheaper than last year’s.

Airlines work off long-term fuel contracts, so they’re not able to benefit from cheaper oil prices as quickly as drivers can. But it’s been months since jet-fuel prices began their steep decline, and airlines have shown little interest in returning any of their savings back to fliers.

So why aren’t airlines sharing the wealth? Simple: They don’t have to. Demand for tickets hasn’t dropped, and most planes are close to full.

For that, travelers can thank years of bankruptcies and mega-mergers (remember AirTran? Continental? Northwest?), which have further strengthened airlines’ grip on American skies.

There were nine major domestic carriers in the United States 10 years ago. Now there are four (American, United, Southwest, Delta), and they’re not exactly worried about an upstart jumping in to compete. Running an airline is exorbitantly expensive, but starting a new one is even worse.

“We are unquestionably living with an air travel oligopoly,” Vinay Bhaskara wrote in Airways News column. “A fare war requires some sort of competitive response to low fares, and a broad-based competitive response to (ultra low-cost carriers like Spirit Airlines) doesn’t appear imminent.”

Airlines say their pricing is necessary for the renewal of their air fleets, the reduction of their debt and the health of their workforce. They add that other costs have bumped up besides fuel, including worker wages, airport rents and landing fees.

“The fact is more people are flying today than in the past seven years because of the continued affordability of air travel,” said Melanie Hinton, a spokesperson for industry trade group Airlines for America. Flights are still “one of the best bargains for consumers, and airlines are meeting this demand.”

Nearly all the savings, airlines have said, are going toward buying new planes, launching new routes and upgrading airport lounges and ticket counters; that is, all the money not yet returned to shareholders, executives and employees.

As John D. Rainey, United Continental Holdings’ executive vice president, told analysts last week, “The opportunities that we have to improve our business with the type of cash flow that we can generate (off cheap fuel) are huge.”

But experts say unsinking travel costs won’t change as long as airlines exhibit total, unrivaled control. Without any pressure from passengers or competitors, they said, airlines won’t see any reason to change their tune.

“Airlines have the pricing power,” Bob Mann, a former American Airlines executive, told Bloomberg in October. “Why are they ever going to give it up?”