Stories as juicy as jazz musician Billy Tipton’s don’t come around often. Tipton, a much-divorced father of three adopted boys, was at best a minor figure in the music world, but he became world famous in 1989, when he died and it was discovered that he was a she. For more than 50 years, he had strapped down his breasts and slipped a little something extra into the jockstrap he always wore. He was taken by almost everybody as a man. Even most of his wives said they thought they’d married a man–and had intercourse with him, often.

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Suits Me finds a context for Tipton in a detailed evocation of the small-time music scene. He seldom recorded; he made his living playing in house bands for radio stations and by touring Oklahoma and the midwest in combos that specialized in imitating Benny Goodman’s sound. Middlebrook researched the times and places, then filled in the blank spots with educated guesses. “Billy did not write a memoir or leave a letter marked with the instruction ‘To be opened after my death,’” Middlebrook notes. “We will have to substitute imagination for the absent documentation. Perhaps what happened went something like this.” And away she goes. Most of the time she convincingly passes off her hunches as facts, and all but erases the line between biography and novel. Though it’s clearly calculated not to seem blatantly exploitative, Suits Me has all the suspense and voyeuristic kicks of a true-crime book.

The early parts of Tipton’s life were the most difficult to research since so much time has passed, and as a result his youth is the liveliest part of the book–Middlebrook makes up for what she lacks by turning out a thorough and entertaining piece of ethnography. Delving into our purportedly simpler past, she finds in Prohibition-era Oklahoma City a thriving, populous lesbian community, though she notes that such terminology belongs to our age, not Tipton’s. In Billy’s time, “invisibility was promoted by the very absence of such categories. An individual could therefore be regarded merely as eccentric, rather than as a member of a social minority or, worse, as pathological.”

Maybe Middlebrook doesn’t want to concede Tipton’s failings because they might somehow suggest that gender roles really are biologically determined after all. Suits Me would seem a more honest book if it wasn’t so preoccupied with political positioning. But maybe honesty is the least appropriate approach to the story of Billy Tipton, who had such a selective way with the truth. Because he rarely recorded, his artistic legacy survives mainly through the scripts for skits he performed in his act. “When did you first begin to like girls?” one of his sidemen would ask. “When I found out they weren’t girls,” came the answer. Another gag ran “How many sexes are there? The male sex, the female sex, and the insects.” Suits Me is at its best when, like Tipton onstage, its wisdom about gender doesn’t stop the show.