WASHINGTON — For those who fly, the squeeze has become the way to beat the system.

"We take the maximum amount on board and squeeze it in," said Susan Williams, explaining how she and and her family avoid baggage fees on flights from Reagan National Airport.

The art of the squeeze is a matter of measurements. When Ross Davis flew to San Francisco last week he paid $25 to check his larger bag but squeezed his other bag, five inches smaller, into the overhead compartment.

American taxpayers are feeling the squeeze, too, even those who never board an airplane.

When the major airlines began charging fees for baggage a few years ago, the rationale they announced was straightforward: Fuel prices had spiked dramatically. Rather than increase ticket prices just as dramatically, airlines would charge for baggage.

Since then, they have collected $12.8 billion for something that once was free.

That has allowed the major airlines — called the legacy carriers — to keep their ticket prices competitive with low-cost airlines.

For taxpayers, however, here is the catch:

There's a 7.5 percent federal tax on every airline ticket. The money goes into a fund that pays for the air transportation system: airports, capital improvements and the operation of the Federal Aviation Administration (FAA).

But in nine of the past 11 years, the amount of money flowing into that fund — mostly ticket-tax revenues — has fallen short of projections. When that happens, Congress can increase general fund contributions to cover the FAA's budget. In both fiscal 2009 and 2010, Congress appropriated an additional amount of almost $1 billion.

When the airlines kept ticket prices down by shifting $12.8 billion to baggage fees, they also saved almost $964 million in federal taxes they would have owed if they had hiked ticket prices by that amount.

Was it a windfall, or was it salvation for a beleaguered industry?

"Last year, our profit amounted to about 77 cents per passenger," said Jean Medina, spokeswoman for Airlines for America, the leading industry trade group. "It's a razor-thin profit margin, so any additional taxes on that is certainly not helpful to the industry and certainly not helpful to the consumer."

The first dozen years of this century have been a virtual nightmare for the airlines. First came the Sept. 11, 2001, terrorist attacks that grounded flights for a while and left the public skittish about flying for even longer. Then the cost of fuel nearly doubled by 2008, increasing the share of operating revenue that it gobbled up from 10 percent in 2001 to 35 percent in 2011.

Next, the deepest recession since air travel became central to American life made matters even worse.

More than 50 passenger and cargo airlines went bankrupt, the legacy carriers began to merge in order to withstand competition from low-cost airlines, and every airline became so efficient at managing its fleet that planes with empty seats became the exception rather than the rule.

As baggage and other fees mounted, the Department of Transportation (DOT) stepped in to make sure that passengers weren't being beguiled by advertised low fares that didn't reflect the true cost of a trip. It directed airlines and ticket agents to disclose baggage fees upfront in online advertising and during the reservation process.

While still too bruised to wax optimistic, the industry seemed to be regaining its footing in the second quarter of this year. Federal data released last month showed that all the major airlines made a profit in the quarter, after mixed results for several quarters.

Together, the airlines posted $2.3 billion in operating profit. But that does not take into account taxes, interest payments and investments outside the core business. Net profit, which does account for those other outlays, was a less imposing $647 million, Medina noted.

"Any profit is better than a loss, but if you look at the full year we're still a billion in the red," she said, pointing to a net loss of $1.7 billion in the first quarter.

A second untaxed fee has been almost as lucrative for the airlines. Though fees for changing reservations have been around longer than baggage fees, income from them has more than doubled in the past six years, netting almost $11 billion in revenue since 2007.

In the second quarter, airlines collected $932 million in untaxed baggage fees and $661 million in reservation change fees, both record-high amounts, the government reported. It does not break out the other new untaxed airline fees for premium seat selections, early boarding, food, beverages, pillows, blankets and entertainment.

A report by the DOT's inspector general last month quoted industry sources in estimating that on average, a passenger paid $22 in round-trip fees in 2010, up from $3 in 2000.

The fragility of the industry, a pressing need to fund multibillion-dollar aviation advancements and overarching concern about the federal deficit weighed on Congress last year as it moved forward with a major FAA funding bill.

At a hearing, several senators asked Gerald Dillingham of the Government Accountability Office how much could be raised by taxing baggage fees. About $240 million a year, he estimated.

Pressed by reporters afterward on whether he was considering that option, Finance Committee Chairman Max Baucus, D-Mont., said, "Not this time."

Asked last month about his current thinking, Baucus said he continues to look at the issue and all revenue options are on the table.

Dillingham recalled that there wasn't much interest in taxing the fees more than 18 months ago. But with revenues from baggage and change fees amounting to $23.7 billion over the past six years, and that untaxed income setting records every quarter, he said Congress may reassess its position.

"The amount of money that's involved is steadily increasing, and that may change some minds on the Hill," Dillingham said. "In my opinion, if that number continues to grow, the interest in having some of those funds be available to the aviation trust fund would also grow."

Whether the fees become a tax target when Congress next takes up aviation funding may depend in part on the stability of the airline industry. Already heavily taxed on tickets and fuel, and saddled with numerous fees, the airlines will underscore that they contribute an estimated $1 trillion in economic activity each year and employ almost 10 million people.

Medina points out that they lost $55 billion and 150,000 workers in the first decade of this century.

The squeeze to escape baggage fees by loading up the carry-on luggage has been blamed for longer lines at airport security checkpoints and occasional delays when every available nook in the cabin has been crammed full without finding room for it all.

Two airlines, Spirit and Allegiant, have begun charging passengers for some carry-on bags, too.

For some travelers, the fees are the cost of convenience.

Craig Furuta's job has him flying all over the country, and says he sometimes brings home more baggage that he left with if he finds things that he can't get in Washington.

"Such as, I bought a suit in London that I couldn't get here in the States, or buying certain jams and jellies — the local stuff is always the best stuff," Furuta said.

He had to lay out additional cash recently to check an overweight bag on US Airways.

"I was flying from Orlando, and I had it overweight because it was packed with souvenirs from Disney," he said. "It was $50 and it was worth it."