After more than three years of debilitating downsizings and quest upon quest for greater efficiency, finding the next wave of profitable growth is again at the top of the CEO agenda—but with some unique twists.

In the past, growth-seeking companies looked to diversification, the next hot market, or building up their weaker businesses. But this time around they are focusing on adjacencies to their strongest businesses, such as moving from products to services, expanding into a major new geography like China, or launching a new business based on a core technology or skill.

Certainly many of the growth success stories of the past decade have been triggered by adjacency moves: IBM's push into services or the global expansion of Vodafone from its base in the U.K., for example. But what is not often recognized is the extent and cost of flawed adjacency moves and the hidden dangers that lie therein. Our research on hundreds of adjacency moves over the past 15 years found that more than three in four failed to deliver on their promise of sustained, profitable growth.

Yet some companies had a much higher success rate, as if they had mastered a "new math of profitable growth." Their skill extended to handling more moves, anticipating them earlier, executing them faster, and making them pay back more often. Often competitive differences on these dimensions made all the difference between stagnating in the pack and achieving true breakout. Three key disciplines were central to their successes:

— Customer-driven innovation. Over 80% of the most successful adjacency moves came not from corporate idea sessions, or investment banker proposals; they came from drilling down deeply into core customer needs. In the past few years, Procter & Gamble has rejuvenated its Crest dental-products line through a "bring the dental office into the home" strategy that led to the launch of several $200 million products, including the Spin Brush and White Strips. CEO A.G. Lafley's focus on growth from the core has caused these deeper probes into historic core customers, and gushers of growth have been discovered.

— Relentless repeatability. Hitting on a repeatable formula for adjacency expansion was central to the success of 70% of the best performing growth companies. Nike and Reebok were neck-in-neck little more than a decade ago. Yet Nike hit upon a repeatable formula blending shoe performance, the management of sports icons, and a unique supply chain for adjacency expansion that propelled them from basketball to soccer to golf. Reebok, by contrast, was like a typist randomly hunt-and-pecking at the keyboard of growth, never finding the combination. In the intervening time, Nike has increased its value by 38 times while Reebok stagnated.

— Reinforcement of the core. New growth opportunities do not exist in isolation, but derive much of their value from how they reinforce the core. The best companies were the most rigorous at mapping out how this occurs. When UPS believed it had a major growth opportunity in delivery and logistics of critical parts it assigned 60 people full time to define where the new business needed independence, or integration with the strong core package delivery business. Today the service parts logistics business, a true adjacency, has grown from start-up to nearly $1 billion in five years.

— Growth from discipline. On the surface, the two seem in opposition. Yet even in individual human endeavor, like the sculpture of Rodin, or the Renaissance work of da Vinci, one finds intensely disciplined preparation married to bursts of creativity. One can only hope that this time around the lesson will be discipline first, then growth, as companies explore the enticing but dangerous territory beyond their core.

Mr. Zook, head of global strategy at Bain & Company, is the author of "Beyond the Core," out next month from the Harvard Business School Press.