(FORTUNE Magazine) – IT'S ONE THING FOR FORTUNE'S Fastest-Growing Companies--with median annual sales of just $582 million--to increase revenues and profits by double-digit percentages. It's quite another for the giants of the FORTUNE 500, with billions in sales, to grow briskly. "Growth is the most difficult thing," says Michael Patsalos-Fox, who chairs McKinsey & Co.'s Americas division. And the most perilous: McKinsey studied the 100 largest FORTUNE 500 companies of 1984 over two business cycles (1984--1993 and 1994--2003) and found that those whose revenue growth trailed GDP growth for an entire cycle were five times more likely to be acquired or go out of business than were the faster growers. So how do the big boys continue to lift the top line? The lessons from these three Hall of Famers encompass the basic, the inspired, and the excruciating. What unites them all: that none of it happens by chance.

P&G: Playing to strength. A.G. Lafley knows how corporate giants grow--or fail to--better than practically anybody. As chairman and CEO of Procter & Gamble and a director of General Electric and General Motors, he's seen some of America's biggest players struggle with the challenge, up close and personal. "The most precious kind of growth," he says, is organic growth--top-line expansion of your core business, without reliance on acquisitions. "You want to grow your core assets, because you understand them the best," Lafley explains. If you can't, you've got trouble.

The organic growth target at P&G: 4% to 6% annually. With P&G's global consumer goods markets expanding only 2% to 3% per year, that's no easy task. Yet P&G has hit or exceeded its goal year after year under Lafley's leadership. How?

The answer starts with focus: Under previous CEO Durk Jager, rapid-fire product launches distracted managers from old-line franchises like Crest and Pampers. Those big brands suffered. "All businesses had equal rights to capital and people," recalls CFO Clayton Daley Jr. Lafley, 58, had a different idea--channeling resources to the company's areas of strength. "What are you really good at?" he asks. "We're good at building great brands, innovating, and leveraging size."

A case in point is P&G's big bet on beauty care. "People were asking, 'How the hell are we going to compete with L'Oréal, Estée Lauder, and Shiseido?'" recalls Lafley. But as a former head of the global beauty business, he knew the margins were sweet and the growth potential high. "Olay was affectionately known as Oil of Old Lady," says Lafley. Today Olay --stodgy and barely profitable when P&G bought it 20 years ago--has emerged as one of the company's fastest-growing brands. Susan Arnold, who runs P&G's health and beauty business, has been aggressive about importing innovation to improve new-product flow: "A.G. wants us to derive 50% [of our new ideas] from outside P&G," she says. A French wound-healing technology in Olay's Regenerist line, for instance, helped pump up Olay's volume 30% in the past year. Health and beauty care today represents 48% of P&G's revenues and 53% of its profits, vs. 36% for both in 2000.

If growth from the core is key, why is P&G acquiring Gillette? "We don't need to," Lafley insists. The $57 billion acquisition makes sense, he says, because it will enhance organic growth going forward. Gillette's market--men's grooming--is expanding faster than P&G's overall market. Plus, he says, P&G can help Gillette's business in China, while Gillette will boost Procter in India and Brazil.

LOWE'S: Discipline matters. By most key measures --sales per square foot, operating margin, return on invested capital, overall revenues--Home Depot is a stronger company than Lowe's. So why has Lowe's stock been stronger over the past five years, tripling vs. Depot's 22% decline? One word: growth.

Sometimes it's good to be No. 2. "Customers want a choice," says Lowe's CEO Robert Niblock, "and if there's a niche where the No. 1 player isn't competing effectively, we fill it." Niblock, 42, wasn't at the company 16 years ago when management made the key decision that has defined Lowe's ever since. The top brass argued for months about trying to make the company the biggest home-improvement retailer. Instead they chose a different vision: to "be our customers' first choice for home improvement in each and every market we serve." They shifted from opening small stores in small markets to building mega-outlets with brighter lights and wider aisles. They won over female customers--important because, according to Lowe's research, women make 80% of home-improvement purchase decisions.

The fundamental strategy of being best in each market has fueled Lowe's unmatched per-store sales growth--the critical measure for investors. Sanford Bernstein analyst Colin McGranahan notes that Home Depot has been strengthened by imitating Lowe's (building brighter, cleaner stores, for example), but that Lowe's has another advantage over Depot: "They have a lot of room to grow without cannibalizing themselves," he says. With 1,125 stores in the U.S., "we can put in 1,800 to 2,000 total," Niblock figures. "And if we add other services and product categories, that number may grow."

Niblock is pursuing international expansion, but it's modest: six to ten stores in Toronto by 2007. Some analysts say Lowe's should buy a chain to catch up to Depot, which already operates 123 Canadian outlets, but Niblock disagrees. Unfazed at being neither biggest nor first in the market, he tells his managers, "Be mindful of what all your competitors are doing, but focus on the customer every day."

FEDEX: Bold strokes. Fred Smith, 61, has had a knack for recognizing change and creating new markets ever since he founded FedEx in 1971. A student of topology (a branch of mathematics concerned with geometric configurations), he figured out that a hub system could be built to ship products anywhere overnight, guaranteed. Experts doubted his approach back then, as did others three decades later when he made two big acquisitions--Caliber Systems and American Freightways--to move FedEx into the freight business. But FedEx transformed freight transport with tracking technology and money-back guarantees and today leads UPS, its bigger rival, in that lucrative business. "Fred is a field-of-dreams capitalist," says A.G. Edwards analyst Donald Broughton.

Such bold strokes require a leader who has the guts to bet on uncertainty. "If the CEO isn't going to do it, who is? Probably your competitor," Smith says. There may be no better example than FedEx's 1989 investment in China. Skeptics deemed Smith premature, if not crazy, for paying $895 million to acquire air-cargo firm Flying Tigers. But Smith, an avid reader of history and demographic studies, says he was convinced that "entrepreneurial China would reassert itself. Deng Xiaoping was clearly stating that China had to move to a market-based economy." Today China is the fastest-growing market in transport. FedEx, which dominates the U.S.-China express market, is expanding business there 50% annually.

Smith is still making big bets. He was in Guangzhou last month, announcing plans for a new Asia Pacific hub at a cost of $150 million. Smith chose Guangzhou because, he says, "one-third of the total exports of China are out of [that area]." He aims to dominate delivery of high-value items like semiconductor chips, PCs, and iPods--far more lucrative than shipping documents. His other new venture, the $2.4 billion purchase of Kinko's, is struggling. But Smith says he envisions FedEx Kinko's becoming America's back office, eliminating the need for companies to have in-house copying facilities--or even offices for sales reps. Given his record of confounding skeptics, investors are cutting him slack. Says Broughton: "The ball fields that Fred Smith built decades ago are now producing so much cash, they can fund whatever dreams he's chasing."

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