Weiss was 14 when Wilensky killed himself, and her evocation of the era’s parenting is rich. That decade, seemingly so recent, was a time when Manhattan parents were apparently perfectly happy to send their daughters off with a coach who offered extra lessons on the weekend, free, to his talented players. Whereas other coaches were demanding and even harsh, Wilensky, in a brilliant move, styled himself as fun: “an entertainer,” the kind of guy who showed up for practice on roller skates in a clown nose and a tutu. Weiss makes abundantly clear the respite Wilensky’s approach provided kids like her — from academic, social and parental pressures to achieve and conform. “Manhattan kids,” she notes, “aren’t used to being treated as kids — and Gary knows this.” Wilensky’s nonjudgmental on- and off-court presence — his noncondescending friendship and understanding, even the fact that she could chew gum and listen to cheesy songs in his car without being criticized — cemented the aging pro’s attraction for the teenage Weiss. Yes: Wilensky’s deal with the parents included his driving the girls back and forth, often taking them out to lunch or supper afterward.

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Occasionally these afternoons took a bizarre turn — such as the time Wilensky took Weiss and her playing partner into an erotic bakery. Rather than traumatizing Weiss, Wilensky’s matter-of-factness about the chocolate penises makes Weiss feel that she has passed a maturity test — that she’s been given a privileged glimpse into the adult world from which she is usually, conspiratorially, barred.

The book’s larger irony is that if Wilensky, the secretly deranged coach, is a somewhat oddball but consistently supportive presence in Weiss’s life, Weiss’s mother in these years is her emotional quagmire. Determined not to ignore her daughter the way her mother had her, the scrappy Mrs. Weiss works indefatigably to help Weiss look pretty, booking the weekly salon appointment to have her curls straightened, telling her, of the bone in her nose, “When your face stops growing, that’s when we’ll fix it.” Another thing that has changed mightily since the 1990s is received standards of beauty; one feels painfully aware of how the teenage Weiss and her mother were both victims of the time, her mother’s well-meaning efforts contributing to Weiss’s uncertainty and her craving for the unwavering approval offered by an adult like Wilensky.

Memoirs that have a ripped-from-the-headlines event as their catalyst often need to pad the narrative to reach book length. Weiss gets surprisingly good mileage out of a trip to Wilensky’s hometown, Roslyn, Long Island — his yearbook page shows him to be that guy everyone knew in high school: shortish, “almost handsome” and a whiz on the dance floor. Her forays into the psychology of stalkers feel more mechanical — in part because what was unheard-of in the ’90s is now trite fodder for reality shows — and her dutiful interviews of her fellow “Gary’s Girls” might have been condensed rather than reported moment by moment. What we could have used another passage or two of, on the other hand, is the actual tennis. While Weiss tantalizingly gives us a couple of scenes on court to establish Wilensky as a coach, we learn virtually nothing of her as a player beyond the fact that, unlike Wilensky’s eventual victim, she wasn’t a ranked junior.