(FORTUNE Magazine) – OF COURSE we can't grow right now; our markets are in the dumps.'' Next time the company apologist tries to sell you that line, tell him you aren't buying. Tell him the best companies learn to do more than endure the worst times. They thrive. Case in point: Unifi, a North Carolina textile manufacturer that has grown into a billion-dollar beauty even as its markets turned downright ugly. Unifi -- rhymes with ''superfly'' -- is the world's largest producer of textured polyester, the yarn that is spun into that butt-of-countless-jokes fabric that had its heyday around the time of Billy Beer and smile pins. As polyester fell out of fashion, demand for filament poly, the stuff that is made into polyester yarn, dropped from 1.4 billion pounds in 1975 to 650 million in 1985. ''The market went to hell in a bucket,'' says founder and Chairman Allen Mebane (rhymes with ''ebbin' ''). Mebane, 64, who prefers tailored suits to double knits, comes across as a courtly Southern gentleman, but in the textile biz he is known as opportunistic, shrewd, and aggressive. ''Guilty as charged,'' he confesses with a twinkle in his eye. He mostly takes care of strategy and leaves day-to- day operations to CEO William Kretzer, 47. Mebane didn't just stand by and watch Unifi unravel. He grabbed market share, found new applications for his yarn, and marched into the nylon and cotton businesses. He figured that only a few of the 50 or so U.S. manufacturers would survive the shrinkage in polyester demand. So he decided to try to consolidate a fragmented market by spending heavily on the latest equipment to drive down costs and improve quality. The money came mainly from internally generated cash, bank debt, and public offerings. The new equipment improved production speed and enhanced quality, making Unifi the lowest-cost producer. That squeezed out competitors for which polyester was just one of many businesses. ''It was easier for them to write off everything in one quarter than to keep spending for ten,'' says Mebane, sitting on a couch in the Greensboro headquarters, his King Charles spaniel, Jack, in a chair beside him.

Today Unifi has over 70% of the U.S. polyester market. It found new customers in home furnishings and autos. Says John Baugh, a textile analyst with Wheat First Securities in Richmond: ''Unlike other companies, it has a game plan.'' Demand has come back for polyester fabric over the past ten years because of these new markets. And several years ago Mebane pushed into making nylon. This business fits well because it uses similar equipment and the same distribution channels. To succeed, Mebane dusted off the old strategy: Invest in new technology, push costs down, snatch market share. Today Unifi has almost 70% of the hosiery market, and nylon accounts for about $500 million a year of sales. Its biggest customer is Sara Lee, which makes Hanes and L'eggs. Natural fibers were a logical next step. Last year Unifi advanced boldly into the supercompetitive cotton spun-yarn business by acquiring Vintage and Pioneer, two private, fast-growing mills that control 15% of the market. Mebane set out to replicate the usual strategy. But this time a funny thing happened on the way to the bottom line. Demand for cotton apparel slowed because the market became saturated, but capacity remained high. Price weakness and heavy capital expenditures ate into earnings like a boll weevil. Wall Street beat the stock down from $38 to $20 a share; even so, Unifi shares have produced an average annual return of 37% over five years.

Mebane is sensitive to the stock's gyrations: He owns 3.4% of the shares outstanding. But he still believes the best way to weave superior returns for all shareholders comes from his tried-and-true strategy. ''We'll continue to spend to build the cotton business no matter what,'' says the chairman. ''After all, it's not a bad time to go after market share when demand falls apart, is it?''

CHART: NOT AVAILABLE CREDIT: FORTUNE CHART/SOURCES: COMPANY REPORTS, WORLDWIDE CAPTION: UNIFI Greensboro, N.C.