Häagen-Dazs. The words mean nothing in Danish or in any other language, but to millions of ice-cream connoisseurs they translate as the creamiest, richest and best-tasting summer treat in the land. So why the umlaut and the map of Scandinavia on the lid? "We wanted people to take a second look and say, 'Is this imported?' " admits the firm's founder and president, Reuben Mattus. His wife, Rose, thought it up. "We made a name and created a meaning for it," he grins. "It means 'the best.' "

Indeed, the name is virtually the only artificial ingredient in Häagen-Dazs ice cream. It has no preservatives, additives or stabilizers and it boasts only fresh cream, milk and eggs, natural foodstuffs like Madagascan vanilla beans and South American coffee beans, and even real rum for its rum raisin flavor. "We had to get a permit from the government for that," says Mattus, 68.

What sets Mattus' product apart is richness—the result of its low "overrun," the amount of air pumped into it. Häagen-Dazs has a 20 percent overrun, compared with Bassett's 75 percent and Breyer's 92 percent. In the world of ice cream, however, low overrun means high price; Häagen-Dazs cones can cost $1, pints up to $2.29, and quarts a hefty $4.50.

Mattus' method not only licked the overrun, it whipped up new profits. While general ice-cream sales in the U.S. increased a chilly two percent in 1980, Häagen-Dazs' have climbed 125 percent since 1975. This year Mattus expects to sell six million gallons, or $40 million worth.

Mattus has been in the ice-cream business for 60 years. A Polish immigrant whose father was killed in World War I, he came to the U.S. at the age of 7 with his mother and sister. They settled in New York and started selling homemade lemon ice that young Reuben delivered around the Bronx in a horse-drawn cart. They eventually added ice cream to their line, but the business remained seasonal until refrigeration became widely available in the 1940s and ice cream turned into a year-round treat.

Mattus prospered, but by the 1950s the large mass-producers of ice cream started a price war that he couldn't fight. "I realized I couldn't keep up and maintain any kind of quality," he recalls. "I thought maybe if I made the very best ice cream, people would be willing to pay for it."

Thus, in 1960, Häagen-Dazs was born, weighing in at 75 cents a pint to his competition's 53 cents. At first there were just three flavors—chocolate, vanilla and coffee—and they were sold only in gourmet shops around Manhattan. Through word of mouth, plus a healthy dash of snob appeal, Häagen-Dazs has expanded to 19 flavors, including exotics such as carob and cassis. (Vanilla remains the best-seller.) Now all flavors are available throughout the country.

Despite its success, Häagen-Dazs remains a family business. Rose is the company comptroller. One daughter, 42-year-old Natalie, is married to the company's general counsel, Evan Salmore. The other, Doris, 39, originated and runs the booming Häagen-Dazs franchise business, which thus far has licensed more than 92 stores nationwide. Doris' former and present husbands also work for the firm.

Simply being able to afford the $20,000 franchise fee (plus an additional $65,000 to $100,000 for equipment) isn't enough; Doris is particular about the people who sell her product and screens potential licensees. "It's like an extended family," she says, "and we want to keep it that way."

Now Häagen-Dazs faces two premium-priced rivals with names that not only sound exotic but actually mean something: Brooklyn-made Alpen Zauber (German for "Alpine magic") and Früsen Gladjé ("frozen delight" in Swedish), a product of Dolly Madison. The competition doesn't bother the family behind the ice cream which one food critic calls "frozen sin." Exclaims Doris: "Our customers are repeaters. Once they taste Häagen-Dazs, we've got them for life."