American Muslims, especially those in the second generation, say they live in two worlds–the traditional, religious world of their parents and the world of the rest of us. And the success of Primo Moda (Altalib says she’s sold thousands of suits over the past year) is proof that they like it that way. Profoundly unrevealing swimsuits can be found online through a surprising number of companies. One, called Splashgear, based in Huntington Beach, Calif., has a slogan that might raise eyebrows: “Now go get wet!” Another–one that’s generating a lot of buzz, if you can say that of a company that sells full-body bathing suits–is an Australian outfit called Ahiida. Its hooded “Burqini” is available in both slim-fit and modest-fit styles. For Muslim women who prefer winter sports, there’s Capster, a Dutch company that makes fleecy, tight-fitting head coverings for skiers and ice skaters.

Just as Muslims are changing the face of America, American values and customs are changing them. Last year Suzanne Brahmia, who works at Rutgers University, started women-only swim nights at one of the university pools. About 60 women of all ages, including novice swimmers, now regularly attend. The ones who have bathing suits wear them; others wear shorts and T shirts. The modesty, explains Brahmia, is in the single-sex community, the female lifeguards and the paper that covers the windows. Brahmia, a convert who grew up Roman Catholic, a swimmer and a soccer player, believes that swimming is a life skill. She wears a regular tank suit.