If you want to understand the nonconformist culture of Southwest Airlines LUV , you’ve got to start with its holiest site: the shrine to Herb. Walk into the company’s headquarters, located in a five-story gray building next to the Love Field airport in Dallas, go past the front desk, and proceed down a broad hallway until you get to a horseshoe-shaped employee lounge with a soaring atrium. There you’ll find a museum of sorts honoring Southwest’s Wild Turkey–swilling, Marlboro-smoking co-founder and former CEO, Herb Kelleher. In one towering poster on the wall he’s shown hamming it up in a sequined Elvis costume; in another he’s arm wrestling an aviation rival for charity. Push a red button and you can hear a recording of three versions of Kelleher’s famous laugh—the guffaw, the chortle, and the roaring belly buster. On the walls there are embossed plaques with a selection of his favorite sayings, none more emblematic than this gem: “If you rest on your laurels, you’ll get a thorn in your butt.”

The voluble Kelleher, now 84, no longer gives interviews but still comes to the office on a regular basis—and his legend looms large at Southwest. Starting with just four planes flying to three Texas cities on June 18, 1971, Kelleher built a maverick operation that prided itself on charting a different route from other airlines. It wooed passengers with ultra-friendly onboard service, squeezed more flights a day from every plane, and made money not by raising fares but by lowering them—and hence filling seats with folks who could never before afford to fly. Kelleher’s company created the template for other low-cost airlines to follow.

Along the way Southwest evolved from an upstart to a colossus that last year carried 134 million passengers in the U.S., more than any other airline and some 20% of the total. In an industry in which every other major company has gone through bankruptcy, Southwest has never gotten close to Chapter 11 and has made money for 42 straight years. Since it was listed on the New York Stock Exchange in 1977, the airline’s stock has delivered 17.5% average annual returns compared with the 11% average gain for the broader market over the same span. In 2014, Southwest was the top-performing stock in the S&P 500, posting a 122% return.

Southwest Airlines CEO Gary Kelly Southwest Airlines CEO Gary Kelly at the company’s training facility near its headquarters next to Love Field in DallasPhotograph by Nancy Newberry for Fortune

So how has Southwest responded to such a period of extended success? Let’s just say that there won’t be any thorny derrieres in the airline’s executive suite anytime soon. The company is in the process of reworking or jettisoning altogether much of Kelleher’s tried-and-true strategy—with plans to fly in a totally new strategic direction. In fact, after years of consistently outsmarting and outperforming the traditional carriers, Southwest is today remaking itself to operate more like them.

For decades Southwest has flown mainly to small airports in big urban markets, where it faced weak competition and could quickly turn around its planes from landing to takeoff. Now it’s invading America’s biggest, most-congested airports and going nose-cone-to-nose-cone with its newly resurgent big rivals—American, Delta, and United Continental—where they’re strongest. The goal? To attract more of the most lucrative customers: high-fare-paying business travelers flying long distances. “Southwest still has a unique personality, but it’s flying more and more in formation with the Big Three,” says Michael E. Levine, a professor at the NYU School of Law and a former top executive at Continental and Northwest.

The architect of this new strategy is no outsider. Rather it’s Gary Kelly, 60, a 29-year Southwest veteran who’s served as CEO since 2004 (and is revered enough at the company that he has earned his own mini-museum almost as large as Kelleher’s). The big challenge, says the strapping 6-foot 4-inch Texan, is that Southwest’s traditional business—short-haul flights between such cities as Dallas and Houston, or San Francisco and Los Angeles—has declined sharply in recent years and now grows modestly at best.

Southwest’s best opportunities for expansion and profits are in long-haul business travel now for two reasons, explains Kelly. First, long haul is the biggest, fastest-growing segment in U.S. air travel. Second, it’s an area where Southwest is relatively small and that is dominated by the legacy carriers Southwest beats everywhere else. That means there’s a lot of market share for Kelly’s airline to go after. “We had to call an audible, and pivot from being so totally dependent on short haul and leisure,” says Kelly, sitting in his office filled with Lone Star memorabilia, such as a copy of the 1836 Texas Declaration of Independence. “If you’re going to grow, you need universal appeal.”

The success of Kelly’s new flight plan is far from certain. Southwest has long held a wide cost advantage over its rivals, but that gap has narrowed dramatically in the past few years. The traditional carriers are now a lot bigger and more efficient than at any time in Southwest’s history. Since the mid-2000s they’ve engaged in bankruptcy restructurings and epic mergers that have both substantially lowered their costs and bolstered their leverage in the top business markets.

Just as daunting for Southwest as its newly tough competitors, say some industry observers, is the challenge that Kelly’s airline faces in trying to reinvent itself without losing its edge. Southwest has made an art form of no-frills travel, but it has little experience wooing business travelers with generous perks. In behaving more like its rivals, the perpetual underdog risks becoming a member of the club—a profitable but average performer whose fortunes wax and wane with the overall industry.

Kelly dismisses any suggestion that Southwest is mimicking its competitors. His airline will remain on top, he says, by deploying its traditional advantages in the big-city business market. “We’ll take customers from the legacy carriers,” Kelly declares confidently. “Our service levels are the best in the business, our costs are the lowest of the majors, and our beloved brand puts us in a prime position. We’ll grow faster than they will.”

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Wall Street is not quite as sanguine about Southwest’s revamped strategy or its ramifications for the rest of the industry. In fact, earlier this year talk of the airline’s expansion plans spooked investors and helped spark a sector-wide selloff.

On May 19, Southwest made the seemingly innocuous announcement that it was raising this year’s goal for additional capacity from 7% to between 7% and 8%. (Capacity is defined as available seat miles, or the total miles flown by every seat on every plane throughout the year.) That same day, Doug Parker, CEO of American Airlines AAL , the world’s biggest carrier and Southwest’s archrival in the Dallas/Fort Worth market, launched a salvo at discount carriers, stating that American would match any fare the low-cost airlines could muster and fight to keep them from poaching American’s customers.

The combination of Kelly’s new forecast, modest though the increase was, and Parker’s challenge to discounters spread fears that the industry was returning to its bad old ways of buying too many new planes and adding seats far faster than it could sell tickets. That cycle brought collapses in fares and stock prices many times before. By the following day shares in Southwest, American, and United had all dropped about 12%, erasing roughly $10 billion in market value; shares of Delta, which is less involved in the Texas price wars, fell too but not as steeply. Kelly quickly trimmed his capacity forecast back to 7%. But Southwest’s stock and those of its big rivals—other than Delta—remain below their highs from last spring.

There are other reasons to be concerned that a period of sustained health for the airlines could be coming to an end. At an industry conference in early June top execs addressed the growing angst over a revival of the industry’s hobgoblin: unbridled battles for market share. The leaders, including Parker, American’s CEO, trumpeted that the industry had learned its lesson in avoiding price wars and expected that the carriers would keep exercising “discipline” by limiting growth in capacity. Weeks later the U.S. Department of Justice confirmed that it was launching an investigation into “possible unlawful coordination among airlines.”

The industry’s critics argue that the recent spate of mergers has led to unprecedented concentration: The top four airlines now fly three-fourths of all the seats offered in the U.S. market. Though price wars frequently erupt, it appears to many that the airlines are not competing as hard as they would if more big carriers were battling for passengers on the same routes. Case in point: Jet fuel prices dropped 35% in 2014, yet average airfares actually rose slightly. “Increased concentration has pushed up prices,” asserts Chris Sagers, an antitrust expert at Cleveland State University. “When you have just two competitors on a route, and that’s the case on many routes, competition tends to be muted.”

On close inspection, Southwest’s growth ambitions are unlikely to be the factor that undermines the industry’s newfound profitability. Although Kelly plans to expand faster than his competitors, he won’t do so the way investors dread—by purchasing lots of new planes and flooding the market with seats for sale. On the contrary, most of Southwest’s growth will come from two factors. The first is a great one-time opportunity: Southwest’s new freedom to finally fly long-haul routes from its home base in Dallas. (More on that breakthrough later.) The second is the campaign to attract business customers. That will indeed add more flights and seats on long-haul routes, but Southwest is also trimming unprofitable flights, so its total capacity will increase only modestly.

“If you’re going to grow,” says Southwest CEO Gary Kelly, “You’ve got to have universal appeal.”

To better understand why Kelly feels compelled to mess with his airline’s winning formula, it helps to drill down into the numbers. Specifically, let’s compare Southwest’s financial performance for the first six months of 2012, when the industry was emerging from the recession, with the same span this year, a fantastic period for the airlines. For the six-month period ending June 30, 2015, Southwest posted an operating margin of 19.6%, more than triple the number in 2012, and the highest figure since 1980.

That sounds great on the surface. But let’s dig deeper. Southwest maintains about a 25% advantage in costs over the network carriers, measured on cost per available seat mile, or CASM, the expense of flying one seat one mile. The rub is revenues. According to Barclays, Southwest’s revenues for one passenger flown one mile are as much as 20% lower than its rivals’ on long routes. “Southwest is a cost leader and revenue laggard,” says David Fintzen, a Barclays analyst.

Airlines’ costs fall into three main categories: labor, jet fuel, and “all other,” which is chiefly the cost of buying, leasing, and maintaining aircraft. Over the past three years, Southwest’s labor bill jumped $663 million, or 28%. In fact, Southwest’s edge in salaries, wages, and benefits over its big rivals has pretty much disappeared as the legacy carriers have come out of bankruptcy with more company-friendly labor deals.

Southwest has always done a brilliant job controlling its costs in the “all other” bucket, largely because of its unique approach to managing its fleet. It’s the only major airline that flies primarily one basic type of plane. Almost its entire 689-plane fleet consists of Boeing 737s in two varieties, the 737-700 and the newer 737-800. The single-aisle models are close to identical, except that the newer 800 model contains more seats than the 700—175 vs. 143. Using one plane produces big savings in pilot training and maintenance.

The company also gets more work out of each plane than other major airlines. While the so-called network carriers like Delta DAL and American funnel most of their passengers through gigantic hubs where they connect to dozens of destinations, mostly in midmorning and late afternoon, Southwest primarily flies nonstop “point to point” routes evenly through the day. That smooth flow of traffic enables Southwest to keep its planes and crews in the air nine hours a day on average, beating its rivals’ airtime by two hours. “That’s like getting one airplane in five for free,” says Randy Babbitt, Southwest’s chief of labor relations.

Southwest also has a history of skillfully hedging its exposure to swings in the price of jet fuel, a Kelly specialty. In the mid- to late-2000s, Southwest saved several billion dollars by locking in years of supply at bargain prices as oil soared to over $100 a barrel. But when prices plateaued at high levels, Kelly—figuring they had pretty much peaked—sharply reduced purchases in the futures market. So when prices began to plummet last year, Southwest took only minor losses on hedges and pocketed most of the cost savings. In the first six months of 2015 it spent just $1.88 billion on jet fuel, compared with $3.1 billion over the same period in 2012, a savings of 39%.

Southwest Airlines CEO Gary Kelly Big smiles are wonderful but maybe not enough. While Southwest is radically changing its strategy, it’s only tweaking its service for business customers.Photograph by Nancy Newberry for Fortune

When that windfall is excluded, Southwest doesn’t look like such a champ for its performance in the first six months of 2015. Its operating profits rose just $179 million, a total gain of 5% over the total from 2012. Its operating margin, excluding fuel costs, actually declined from 41% to 39%.

Those numbers point to Southwest’s big challenge: It’s not yet adding enough business travelers to its fare mix. From the first half of 2012 to the same period in 2015, Southwest’s average passenger fare increased just 6%, to $158, even though it was adding longer flights to lure business customers.

Meanwhile the network carriers are closing the profitability gap. For the first six months of 2015, Delta’s 19.3% operating margin virtually matched Southwest’s. In the past Southwest typically enjoyed a seven-percentage-point advantage in operating margins on its domestic business. But in recent years, according to a study by Barclays, that edge had shrunk to about two percentage points.

Kelly revealed his general targets for business travel to Fortune, and they’re ambitious. He wants to raise the portion of business customers on Southwest from 35% to around 40% over the next five years, moving it closer to the traditional airlines’ fifty-fifty ratio. Kelly also thinks Southwest can lift its “load factors,” the percentage of seats occupied on the average flight, from today’s record 84.6% to 90% over the same period. By Fortune’s calculation, that combination would raise the average number of nondiscount passengers on a 175 seat 737-800 from 52 to 63 and enormously increase a flight’s profitability.

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Given the shifting landscape in air travel, Kelly’s gambit makes sense. The central issue for Southwest is how to adapt its basic product—whether it can provide the upscale perks that will lure business passengers from, say, Delta or American and not alienate its loyal customers.

In the past several years Southwest has invaded half-a-dozen major airports it had previously shunned, including Reagan National near Washington, D.C., LaGuardia and Newark in the New York City area, and Logan in Boston. To fill more seats, Southwest is also echoing the majors by offering far more connecting flights through such hubs as Midway in Chicago and BWI outside Baltimore. In general, the longer the flight, the greater the competition. At the major East Coast airports that Southwest has invaded, that’s precisely what it’s facing.

The most notable example is Southwest’s showdown with Delta at the world’s busiest airport, Hartsfield-Jackson in Atlanta. Southwest purchased AirTran in 2011 to gain a foothold in that crucial market. AirTran used Atlanta as its hub, connecting passengers to dozens of small cities. Now Southwest has converted many of AirTran’s flights to nonstop routes to major cities such as Houston, Denver, and Los Angeles in an attempt to steal Atlanta-based business travelers from Delta.

So far, however, Delta is winning the contest. It still controls around 80% of the seats sold in Atlanta and hasn’t yielded much to Southwest on routes where the two airlines compete. For flights from Atlanta to Denver, a Southwest stronghold, Delta sells 50% of the seats, more than twice Southwest’s share. And the picture is similar for service to Phoenix, Houston, and Los Angeles. In Atlanta, according to Barclays, Southwest’s revenues for each seat it flies are 17% below its big-city average, and its sales growth in Atlanta lags well behind Delta’s. But Southwest, says Kelly, is only beginning to exploit Atlanta’s potential. “Atlanta is a developing market,” he says. “It will improve significantly over time.”

On leisure routes, Southwest has for decades won customers by sharply lowering fares. Its latitude for dramatically underpricing the competition is more limited on long flights, because the farther it flies, the less cost advantage it enjoys.

Southwest Airlines CEO Gary Kelly Southwest is the only major airline that primarily flies one basic type of plane. Using one plane produces big savings in pilot training and maintenance.Photograph by Nancy Newberry for Fortune

So Southwest is relying on a couple of long-standing strengths to attract road warriors: its fee-free bookings and ultra-friendly customer service. Southwest is the only airline that charges neither for checking bags nor for changing a ticket. If a business traveler checks two bags on a roundtrip flight, he or she typically pays an extra $200 on most airlines. On Southwest those suitcases fly for free. In fact, for customers who drop off even one bag, Southwest offers the best deal 60% of the time, rising to 88% for two bags, according to corporate travel consulting firm Topaz International. Customers can also change a ticket at no extra charge or, if they cancel a flight, get full credit for another trip. That can be a big money saver for business travelers, who make lots of last-minute changes. Southwest has also greatly enhanced its frequent-flier program, called Rapid Rewards. Starting in 2011, Southwest was the first among the four biggest airlines to award points not by number of trips or miles flown but by dollars spent, a big inducement for folks buying pricey tickets.

Most of all, Southwest wins loyal fans with its vaunted customer service. Abigail Johnson, co-founder of Silicon Valley public relations firm Roeder-Johnson, regularly flies Southwest from San Jose to LAX and says she mainly takes Southwest even when flying cross-country. “What I like best is the attitude of the flight attendants,” says Johnson. “I’ve taken 1,100 flights on Southwest and maybe met two or three flight attendants who were unpleasant. On other airlines you hear them complaining all the time.”

Big smiles are wonderful but maybe not enough. While Southwest is radically changing its strategy, it’s only tweaking its service for business customers. Southwest’s model was originally designed for travelers who pass quickly through airports, not road warriors who practically live in them. The airline doesn’t provide first-class cabins or airport lounges. Nor does it offer assigned seats. All the rows are the typical coach three-across configuration, and all the seats are the same. Customers who pay the highest Business Select fares get to be among the first 15 to board. But many business passengers get stuck in the classic Southwest “cattle call” boarding process and must scramble to get a window or aisle seat.

By contrast, the network carriers’ core franchise is long-haul business travel. Business travelers may hate the delays, the sometimes rude service, and the packed planes, but they keep coming back for the key perks. For the trip from Atlanta to LAX, an executive flying business class with Delta can first phone customers from the Sky Club lounge while waiting to board, then slide into a lush, two-across seat onboard with plenty of room to deploy his laptop.

It’s certainly possible that Southwest will, for the first time, offer the type of premium seating JetBlue JBLU recently introduced with its Mint product. But for now Kelly says he has no plans to change a model that has always thrived on simplicity. If Southwest does offer first-class cabins, it will win higher fares but also make sacrifices. For example, travelers on commuter routes won’t pay a premium for first class, yet the planes will offer fewer seats because first class takes more space. If Southwest goes with two types of planes—one with first class, one without—it will lose the flexibility to quickly substitute one aircraft for another on any route.

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Even as Southwest wrestles with these strategic questions, it’s pushing into another new frontier: international travel. Southwest is going abroad for the first time in its history. It was the AirTran purchase that gave Southwest a base of foreign routes. Now Kelly is building international into a major growth engine with an aggressive expansion in AirTran’s prime overseas market, Latin America. The region is one of the world’s fastest-growing air-travel destinations, yet competition on routes from the U.S. remains muted. Today the biggest U.S. hub serving Latin America is United’s operation at Houston International. United currently holds an ultra-powerful position on nonstop flights to Mexico City, Costa Rica, and other prime destinations.

Going international is another way to woo business travelers. The legacy carriers enjoy an especially wide advantage over Southwest in corporate deals with Fortune 1,000 companies. “Those large multinationals want access to a global network,” says Bob Brindley, a principal at Advito, a firm that advises corporations on managing their travel. “It’s a big component of what they require. The Big Three offer that, and Southwest doesn’t.” Kelly is trying to close that gap.

Southwest is preparing to challenge United in Latin America by opening a new $156 million international terminal at Hobby Airport, his airline’s Houston base. Kelly says he will slash fares to Latin America from Houston by about 40%. By 2020, says Kelly, Southwest could serve as many as 50 cities in Central America and northern South America. By Fortune’s estimates, Southwest could capture 5% of the nearly $60 billion projected market for travel to Latin America and the Caribbean, adding $3 billion in revenues. That alone would lift Southwest’s projected growth rate from 5.5% to well over 7%.

There’s another growth opportunity for Southwest that’s much closer to home: Love Field. Until the early 1970s, Love Field was the principal airport for the city of Dallas; President Kennedy’s fateful final flight landed there in November 1963. When the cities of Dallas and Fort Worth unveiled their plan for the new DFW in the early 1970s, a major condition was to shutter Love Field, which was slated to become a public skating rink.

All the other airlines agreed to move, but Kelleher refused to budge. Southwest won a famous case—upheld by the Supreme Court—that granted it the right to stay. But its rivals succeeded in persuading Congress to pass a law, known as the Wright Amendment, that severely restricted where Southwest could fly from its home-base airport. The Wright Amendment restricted direct flights by large planes from Love Field to just the four states bordering Texas, a list later extended to include three more nearby states. The airline could fly its 737s to Little Rock and Tulsa, but nonstop flights from Dallas to the big business markets such as New York City and Los Angeles were strictly off-limits.

The rules were particularly galling because Southwest’s identity is closely intertwined with Love Field: Its corporate logo is a heart, and its stock ticker is LUV. Upon becoming CEO in 2004, Kelly immediately made it his mission to kill the Wright Amendment. “It was a ridiculous restriction,” says Kelly. “Short haul was shrinking fast. We needed to fly to the big business centers from Dallas.” In 2006, Congress voted to repeal the Wright Amendment—effective October 2014. So as of late last year, Southwest has finally been free “to move about the country” without restrictions.

For many business travelers, Love Field is far more convenient than DFW. It’s just a few miles from the wealthiest enclaves in Dallas, including gilded Highland Park. Southwest has expanded from 120 to 180 flights a day at Love Field and added service to 34 cities, including such prime business destinations as Denver, Reagan National, and LaGuardia. Those flights are now over 90% full. And even though it’s charging low introductory fares for the routes, Southwest is already reaping some of the best margins in its entire network.

At Southwest’s headquarters across the highway from Love Field, a prized ritual is gathering for Monday afternoon “landing parties” on the roof. Employees sip beers while watching Southwest planes touch down at Love Field and hold up signs rating the pilot’s performance from 1 to 10. Kelleher himself is even known to appear from time to time, a tumbler of Wild Turkey in hand. The colorful co-founder’s presence is a reminder of his airline’s glorious past. But under Kelly’s leadership it is attempting a daring change in course. It’s up to Kelly to deliver a 10 of his own—a smooth landing proving that Southwest isn’t merely middling, but still the best. 

A version of this article appears in the October 1, 2015 issue of Fortune magazine with the headline “Southwest’s radical new flight plan.”