That’s what Apple (AAPL) looked like in 1997, when Steve Jobs returned from his 11-year exile to find what Ken Segall calls a “bloated and mediocre” company just 90 days from bankruptcy. How he turned it around is, by now, the stuff of legend.

“He simplified the corporate structure, he simplified the product line, and he simplified the marketing,” writes Segall in his new book Think Simple: How Smart Leaders Defeat Complexity, out June 6. Of course, not every business leader is Steve Jobs, Segall notes, but Jobs “was not a magician. He changed Apple by taking a common-sense step-by-step approach.”

Segall had a ringside seat for that. Working closely with Jobs for 12 years, he led the creative team behind Apple’s “Think different” ad campaign, and made the simple letter “i” synonymous with Apple by naming the iMac. In his long career at ad giant TBWA\Chiat\Day, Segall also cooked up successful global branding campaigns for the likes of IBM, Dell, Intel, and BMW.

In Think Simple, he never quite gets around to spelling out how huge corporations can banish excess complexity. What the book does offer is a thought-provoking view of simplicity in action, drawn from interviews with more than 40 executives (including a few startup founders) Segall calls his “heroes of simplicity.”

Take, for example, global companies’ penchant for designing different products for different geographic markets around the world. Beyond what he calls the “real, profound, and sensible need to be culturally sensitive,” Segall points out that “there are values that transcend culture.” Instead of unthinkingly piling on a different product with different marketing for each country or region, he writes, smart companies aim to line up their product, and their message, with one of those universal values. Apple pulled this off with “Think different”, but companies like Coca-Cola and the most profitable automakers have figured it out too. A fascinating chat with Steve Wilhite — an erstwhile Apple marketing chief who has built global branding campaigns for Nissan, Hyundai, and Volkswagen — looks at the advantages of creating what Wilhite calls a single, simple “brand that travels.”

Sometimes, what appeals to customers as simplicity is, in reality, anything but. Fans know Ben & Jerry’s ice cream for its big chunks of cookies, candy, and swirls. These were, at least initially, trickier to achieve than you might think. “Your classic ice cream machinery is only designed to handle small bits of things,” co-founder Jerry Greenfield explained to Segall. “We were kind of the first to figure out how to add in those big chunks. It’s very complicated to do this on a large scale, but to our customers it looks simple.” Sounding every inch an ad man, Segall notes that even illusory simplicity “has the power to drive a business.”

In companies with strong cultures, simplicity can take the form of a set of ideas that every employee knows and sticks to. The goal is to simplify the structure of a company by eliminating the need for layers of front-line supervision. The Container Store (TCS), for instance, has grown at least 20% annually since its 1978 founding (and has made Fortune’s 100 Best Companies to Work For ranking for 15 straight years). Its so-called Foundation Principles are seven basic rules drummed into each new hire, like treating the stores’ vendors well and exceeding customer expectations.

“We’re not smart enough to tell thousands of employees what to do in a given situation,” CEO Kip Tindell told Segall. “We don’t even attempt to do that. What we do is get people to agree on these very simple ends. Then we liberate them to choose the means to those ends.”

Skeptics might wonder whether the Foundation Principles really get any more day-to-day attention than most companies’ mission statements (read: none). But Tindell insists that these ideas “aren’t just words on the wall. Our people are constantly talking about them. Having these principles is much better than having a bossy boss tell you what to do.” Simpler, too.