Customers who buy sport motorcycles care about peak performance, but an equally crucial selling point is a visual appeal that provokes envy. Ducati holds just 4 percent of the U.S. motorcycle market, selling fewer than 11,000 bikes in the States annually. But its upper-echelon, design-obsessed customers wouldn’t dream of being seen on a mass-produced machine, even though Honda, which makes 300 times as many bikes as Ducati, gives plenty of bang for fewer bucks. One Ducati stronghold—despite its flat, curveless, traffic-choked grid—is Miami, where looks mean everything. “Our bikes are the weapon of choice at the local Starbucks,” says Michael Lock, C.E.O. of Ducati North America.

Ducati’s uniquely Italian sensibility is an enormous asset—and liability. The company was founded in 1926, and the facade of the factory, on Bologna’s Via Cavalieri Ducati, still has its original Art Deco lettering. The geometric regularity of the building’s prewar architecture is echoed in the regimental row of employees’ motorcycles parked outside. At first glance, the factory looks like a relic, but inside, it’s a sleek, high-tech facility. With fewer than 1,500 employees, the place exudes efficiency, despite a decidedly unrobotic assembly line.

Like Ferrari, Ducati has kept its growth in check in order to focus on high-end performance and cutting-edge design. While BMW makes cars, Honda makes lawn mowers, and Yamaha makes pianos, Ducati sticks almost exclusively to producing hand-built, premium-priced thoroughbred bikes in microbrew quantities. “We produce 40,000 motorcycles a year,” says Lock, a youthful exec who works out of a sunny, comfortably cluttered office in Cupertino, California. “Honda makes millions.”

Of course, a bike’s image depends on technology to back it up. “Engineers in Italy have the kind of status that doctors and lawyers do in other countries,” says Pierre Terblanche, a Ducati ­designer. In 1993, Miguel Galluzzi designed Ducati’s top seller, il Mostro—“the Monster”—reputedly built with spare parts Galluzzi had collected from around the factory. Its “naked” design sparked an industrywide revival of exposed engines, frames, and suspensions. A year after the launch of the Monster, star ­designer Massimo Tamburini won buyers’ hearts and wallets with his 916, a bike that dominated the World Superbike race class and, in 1998, earned a prominent perch at the Guggenheim.

Mass-produced models with blistering performance stats are easily affordable. (Kawasaki’s ZX10, which can hit 90 miles per hour in first gear, costs $11,000.) Artisanal production and premium pricing—Ducati’s extravagant new Desmosedici costs nearly seven times as much as the ZX10—work best when the economy is hot, but in the latter half of the 1990s, even as Ducati was attracting such customers as Ralph Lauren and real estate billionaire Sam Zell (who was denied a bid for a 50 percent stake in 1996), the company was trying to ride out a financial slump. T.P.G.’s purchase strengthened Ducati briefly by increasing production, paying bills, and bringing salaries up to date. But the investment firm’s lack of emphasis on Ducati’s exclusivity threatened to prove fatal.

With their majority share of Ducati, the Americans had bragging rights. In hindsight, it’s clear why Cagiva was eager to dump Ducati on T.P.G. In the U.S., Cagiva was an insignificant player with an unknown reputation, and principals Gianfranco and Claudio Castiglioni “were horrible businessmen,” according to motorcycle historian Charles Falco, a curator of the Guggenheim show. “They could get components shipped in only if they paid up front in cash. The only way they could regain solvency was to sell Ducati, since no one in the States really knew what Cagiva was.”