(FORTUNE Magazine) – Flying at 38,000 feet over the Baltic Sea, the chairman of Royal Caribbean Cruises Ltd. grips his leather armrest and mulls a topic that's become irresistible in the post-James Cameron cruise industry: size. "It's not that relevant, really," sighs Richard Fain, who runs the biggest, and the newest, ships in the business. "The size of a ship is just another feature. It's the amenities that really matter."

Fain, who heads the second-largest cruise company, behind Carnival Corp., detests superlatives. So much so that he has banned his speechwriters from using words ending in "-est." But his modesty is curious in the context of this particular trip. Fain, you see, is aboard a charter flight to Turku, Finland, where he is to check on Voyager of the Seas, a 1,019-foot vessel that, when completed in September 1999, will be the largest passenger ship ever built. Planned diversions for the 3,100 passengers tucked inside this 136,000-ton baby include a television studio, a three-story theater, and an ice-skating rink.

Skating rink?

Okay, so the idea of bikini-clad passengers waddling off to practice double axels is a bit...strange. Then again, for better or for worse, cruising today isn't what it used to be--not even five years ago, when Kathie Lee was still belting out jingles for Carnival's "fun ships." Passengers, who once looked like the Astors, then the Simpsons, are skewing more toward the Huxtables. Shipboard fun has evolved from cramped neon discos to cigar bars and 15,000-square-foot spas. The all-night buffet, still a fixture, is upstaged by the champagne and caviar lounge. "The caliber of ships today is much more 'must see' than five years ago," says Peter Oakes, an analyst with Merrill Lynch.

Buoyed by increased consumer spending--not to mention an urchin named Leonardo DiCaprio--the $9 billion industry's 135,000 berths are filling faster, and fetching higher rates, than in the past seven years. A shipbuilding craze, currently under way, will boost passenger capacity 51% by 2003. As $15 billion worth of ships come on line, cruising's traditional demographic, adults aged 40-plus, will grow more than twice as fast as the overall population. Such activity helps explain why cruise stocks are hot. In the past 12 months shares of industry leaders Carnival and Royal Caribbean have shot up twice as fast as the S&P 500. Analysts peg growth rates for the two at 15% or more over each of the next three years.

In this context, then, Voyager's patch of ice--and matching Zamboni machine--is more than a recreational absurdity. It's a bragging point that should help Royal Caribbean attract more passengers who are willing to pay full tariff. It's also a subtle clue about the new customer Royal Caribbean is courting. "Putting an ice-skating rink on a ship," says Fain, "is not exactly a statement that we're going after the graying population of America."

Business must be good when guys like Fain start dissing the AARP crowd--the very folks who used to keep this industry afloat. Another sign of high times: Disney, the master of induced fun, is getting ready to launch its much anticipated--and much delayed--Disney Magic, the first ship in the company's new Disney Cruise Line.

At the moment Royal Caribbean best exemplifies the madness of the industry--and not just because the $2 billion company is building the mother of all ships. Like the Energizer bunny that just keeps going and going, Royal Caribbean has seen its stock price soar even in the face of criminal proceedings. Adding to the intrigue are Royal Caribbean's famously private owners. The Pritzkers, along with another family, own roughly a third of Royal Caribbean's shares.

Since taking command of Royal Caribbean back in 1988, Richard Fain, 50, has quadrupled the company's size. Within the industry the CEO is known as an unpretentious guy who calls travel agents by name and sends them champagne. He is shy, even awkward. ("I hate speaking in public; I'm not good at it," he says.) He devours paperback mysteries and surrounds himself with smart people.

So it seems odd that this CEO, a member of the French Legion of Honor, is mute when it comes to the stain on his otherwise thriving company. Royal Caribbean recently entered a plea agreement with the Department of Justice admitting to violations of the Clean Water Act, for which it will pay $9 million in fines. The company pleaded guilty to eight counts from two separate criminal indictments, admitting, among other things, that it had deliberately discharged harmful quantities of oil into the ocean through an elaborate system of bypass pipes. Fain declines to comment. Apologizing for the infractions in a statement, Royal Caribbean president Jack Williams said the practices, which included falsifying ships' logs to cover up the pollution, were "wrong" and "inexcusable."

Wall Street hasn't seemed to care much. Since the first charges were announced in December 1996, Royal Caribbean's stock has tripled, to a recent high of $73. A dozen analysts have picked up the company; buy-side guys have added to their positions. Royal Caribbean "had bad procedures, which appear to have been largely corrected," says Robert Simonson, an analyst at William Blair & Co. "The [case] hasn't hurt the business at all."

Indeed, Royal Caribbean is having its best run ever. In a bid to expand its middle-market base into the premium segment, the company acquired Celebrity Cruises last July, raising capacity by 64% and advancing revenues by 67%. Analysts expected the purchase to improve earnings, but they weren't forecasting last quarter's 52% increase over the previous year.

Because Royal Caribbean offers a bourgeois product at a bargain price--the average seven-day Caribbean cruise goes for about $200 per person per day--travel agents say the line sells itself. This is especially true for first-time sailors who want a big-ship experience without--how to put it delicately?--the glitz of a Carnival cruise. Interestingly, a new Royal Caribbean ad campaign makes a deliberate attempt to rope in boomer types who might regard cruising as tacky and claustrophobic. The spots show lithe young couples at play on an island. A ship appears only on the horizon.

Asked what the Royal Caribbean brand stands for, Fain has two words: "consistent quality." What he means is that Royal Caribbean's repeat customers--one in four passengers--are assured of getting the same experience every time. They can dance the same limbo and sip the same Coco Loco rum drinks. They can return to Royal Caribbean's private islands, where there are no homeless people, no rude taxi drivers, and no alarming moments.

On Jan. 12, around the crest of Titanic mania, Royal Caribbean had its highest one-day bookings volume ever--21,827 cabins sold. Hooked up to the industry's most sophisticated electronic and online reservations systems, Royal Caribbean's agents by mid-March had sold 75% of the company's inventory. The line, of course, is hoping for a repeat performance next year, when its newest, gigantic ship debuts.

At the Kvaerner Masa Yards in Turku, in a series of Brobdingnagian blue warehouses, the world's largest passenger ship is slowly taking shape under the hands of 500 Finnish workers. It is one of seven Royal Caribbean vessels currently on order, and when completed in 1999, it will be the 18th in Royal Caribbean's fleet.

Wearing a yellow hardhat, Fain surveys the massive steel Lego-like blocks that will form the skeleton of this "post-panamax" boat. At 48 meters wide, the $500 million craft will be too broad to fit through the Panama Canal. The main purpose of Fain's visit is to view a top-secret mockup--a new design element Royal Caribbean is calling the Royal Promenade. This turns out to be a meandering central walkway that opens horizontally onto shops and vertically to balconied passenger cabins.

Fain and his design man, Harry Kulovaara, have talked about the concept for years. Now they whisper like lovers near the model that's been prepared for their visit. "It has the feel of a town center," says Fain, carefully avoiding the word "mall." Gazing from the faux-cobblestone tile samples to the glass-balconied cabins above, he makes a stunning prediction: that guests will pay more for these interior cabins than for ones with ocean views.

Royal Caribbean has long been considered an industry innovator. Back in 1972 the line was the first to offer air-sea vacations, ferrying guests from all over North America to its ships berthed in Miami. But the company is perhaps best known for the Sovereign of the Seas. Launched in 1988 as the largest cruise ship, the vessel featured a five-story central atrium. Dubbed the centrum by Royal Caribbean, the much-copied design element gave Sovereign the added spectacle of height.

With the larger ships come certain economies of scale. As Royal Caribbean's ships expand, for instance, costs for things like marketing and entertainment get spread over many more passengers. But girth also presents certain problems. "As you increase a ship's size, the audience automatically becomes more heterogeneous," says Murray Markin, a travel industry consultant. "It then becomes more difficult to target yourself to a segment, at a time when you're growing rapidly and need to fill capacity."

On this front, Royal Caribbean and others may soon take a tip from Disney--the new industry entrant that's getting a polite, if strained, reception. "We welcome their presence," says Fain, who argues that the Disney Cruise Line will raise awareness among the estimated 90% of Americans who've never cruised. "Disney may make 5% more people wish to take a cruise but can only offer 1% of them a vacation." Indeed, only four shipyards in the world build today's megaships--and all of them have commitments to other companies through 2001. So, Mr. Eisner, take a number.