This is how the business-travel world has changed since Aer Lingus rewrote the transatlantic fare structure last month.

If you walk up to the Northwest ticket counter at Los Angeles International tomorrow and ask to fly to Amsterdam, an agent will put you on a KLM code-share flight and charge you $2,634 plus a $10 at-the-airport ticket fee. The nonstop flight will take 10 hours and 30 minutes. But walk up to Aer Lingus ticket counter and you’ll pay just $595 for an LAX-Dublin-Amsterdam itinerary that takes 13 hours and 10 minutes. In other words, for the 2-hour, 40-minute layover and Dublin connection, you save $2,049.

Or let’s say you’re in Chicago and disgusted by the unseemly collapse of the Cubs. You can walk up to the American Airlines ticket counter at O’Hare tomorrow and ask to fly to Frankfurt. You’ll get a nonstop flight for $2,465 (plus that $10 ticketing fee) and, 8 hours and 40 minutes later, you’ll be touching down in Frankfurt. But saunter over to the Aer Lingus counter and you’ll pay $306 tomorrow for an O’Hare-Dublin-Frankfurt trip that takes 10 hours and 30 minutes. So if you’re willing to invest one hour and 50 minutes to change planes, you’ll save $2,169.

Paris you say? Well, if you’re in Boston, and you’ve given up on Pedro and the Red Sox, head on over to Logan tomorrow and saunter up to the Delta ticket counter. From there, you can catch an Air France code-share nonstop flight to Paris for $1,758. Just 6 hours and 45 minutes later, you’ll be at Charles DeGaulle, where they’ve never heard of Bucky Bleepin’ Dent. But wander over to the Aer Lingus counter and you’ll pay just $452 for a Boston-Dublin-Paris trip that takes 8 hours and 50 minutes. In other words, invest about two hours of your time and you’ll save more than $1,300.

How about that quick hop to London/Heathrow from New York/Kennedy? United Airlines will charge you $732 (plus that annoying $10 fee) tomorrow for the 7-hour, 5-minute nonstop. But you’ll pay just $321 on Aer Lingus via Dublin and the trip will take just 40 minutes longer. Not a bad time penalty for a savings of more than 50 percent.

Those are the one-way, walk-up coach comparisons, fellow travelers. The business-class price comparisons are off the chart now that Aer Lingus has slashed its Premier class fares by as much as 60 percent. New York-Dublin nonstop is now just $1,304 up front; it’s $200 lessfrom Boston to Shannon or Dublin. Just $1,504 gets you a seat up front from Chicago or Los Angeles.

Now, listen, we’re no fools. Nonstops are better than connecting flights, even via a relatively compact and convenient facility like Dublin Airport. But the eye-popping fare differential and Aer Lingus’ bold approach to simplifying coach fares–no more advance-purchase restrictions, no more roundtrip requirements, no more incredibly annoying garbage–put the connecting-flight strategy back on the table. And when you have to make a connection somewhere in Europe anyway, Dublin is now clearly the price leader for the dozens of cities in the United Kingdom and continental Europe that Aer Lingus currently serves.

After all, where do you want to change planes? Heathrow, where traffic is clogged, the terminals are constantly under construction and even BA, with its admirable beyond-London network, requires you to change terminals for virtually every itinerary? Paris/de Gaulle? Are you kidding? Zurich? Great airport, admittedly, but Swiss International’s network isn’t a patch on the old Swissair system. Amsterdam and Frankfurt? Good facilities, of that there is no question, but Amsterdam is a nightmare during heavy traffic periods because Northwest and KLM don’t put enough baggage handlers on the job. And Frankfurt isn’t quite as easy to use as it was in the days of single-terminal operations. Copenhagen and Helsinki are both nice airports, but neither SAS nor Finnair are any more omnipresent in the United States than Aer Lingus these days.

And none of those airports offers what Dublin now does: An airline that gets it. An airline that understands travelers–both business flyers and vacationers–value simple fares above all else. An airline that understands that Byzantine rules and mindless restrictions repel customers and make profit impossible.

Aer Lingus is already profitable after making the transition that the U.S. Big Six has resolutely refused to make since 9/11. And since more than half of the airline’s profit comes on its U.S.-Ireland routes, the new fares and the simplified structure can mean huge bucks for the carrier.

“I’m filling about half of my [24-seat] Premier cabin now,” Aer Lingus executive vice president Jack Foley told me Monday after the new business-class fares were announced. “If I can get to, say, 75 percent load factor, I can make a great return on this. That’s only six more passengers per flight.”

And what about coach, where all those restrictions have disappeared and prices currently start as low as $114 one-way and are capped at $503?

“I’m only telling people what they already know: That a coach seat is only worth so much,” Foley said. “And I’m no longer asking people why they fly, trying to separate the leisure travelers from the business travelers who might pay more. Now I focus on yield per aircraft, not yield per customer. This is a better way to do it, for customers and for Aer Lingus.”

It’s clear that Aer Lingus has gotten the message: Make it simple and easy to buy a ticket and people will fly. And they’ll fly more frequently at prices that a well-run airline can make money selling. Southwest has always known that. JetBlue launched itself five years ago with that message and is now the carrier everyone loves. America West made a deathbed conversion two years ago and is now profitable. Aer Lingus has shown that an old-line carrier, even a small one that is still government-owned and hamstrung by a raft of competitive disadvantages, can leap into the headlines and into profitability, too.

It’s now up to the Big Six to embrace the logic of reasonable fares sold simply. They have to change because now we can fly almost everywhere without them. What part of that do you think the Big Six doesn’t understand yet?