Much to his credit, Gavin casts light on the Baker mythology without submitting to it or exploiting it for trendy theorizing. ''Deep in a Dream'' has no evident agenda beyond journalistic veracity. Gavin, a New York-based music writer and author of ''Intimate Nights,'' a good serious book on the history of Manhattan cabaret, has constructed a meticulous account of Baker's life in and out of music, and he lets the facts fall where they may. Baker abused everything and everyone in his life, most notably his art and himself. Gavin takes no pleasure in guiding us through the circles of hell that Baker traveled with his countless lovers, wives and bandmates, but he has mapped the route, and the trip passes efficiently.

Musically, Chet Baker was never much more than an acolyte of Miles Davis. A natural improviser, Baker could barely read musical notation and never understood the rudiments of the harmonic theories underlying bebop. (Davis, who attended Juilliard, knew exactly what he was doing and what he wasn't.) His vibratoless tone sounds cerebral and detached, impelling hipsters of the Beat era to take his music as a comment on the existential futility of life or some such. He wavered off key and improvised in halting, broken lines, which his enthusiasts took as expressions of angst, while he was generally too stoned to play better. Inevitably for an artist triumphant in a style that is all style, Baker inspired innumerable mimics who mistook the highly demanding discipline of jazz for something anyone could do with the right attitude and clothes.

When he took up singing and found a larger audience with his quiet, fragile reading of ''My Funny Valentine'' (establishing a then-obscure old Rodgers and Hart song as a vocal standard), the Baker imitators multiplied exponentially, and they're still haunting airport hotel piano bars everywhere. Just a few months ago, I went to hear a promising young singer in a Manhattan club. Her boyfriend was sitting near me. She sang about half the set in tune and the other half uniformly flat. ''I have to get her some new CD's,'' the fellow said. ''She's learning too much from Chet Baker records.''

Baker's most enduring legacy, however, may well be his looks: that face or, more accurately, the two irreconcilable faces of his young and old selves, which Gavin commendably resists describing as ''Dorian Gray'' (though he uses a few too many other clichés). ''As much as any recording,'' he notes, the moodily erotic black-and-white portraits of Baker by the photographer William Claxton ''created the Baker image.'' Gavin is so attentive to this key aspect of Baker's appeal that he interviewed the trumpeter's haberdasher, one Charlie Davidson, who takes a knowingly cynical view of his client's popularity. ''Half of it was physical attraction,'' Davidson said. ''I mean, what right did he have to be winning Down Beat polls over Miles and Dizzy and Clifford Brown? Everything was getting so out of proportion.'' Many of Baker's most enthusiastic early fans, Gavin explains, were titillated young women -- and gay men.

The author is fearless in his exploration of the mixed sexuality at play in Baker's life, work and career. When ''Chettie'' was a tot, we learn, his favorite toys were a baby doll and a Tinker Toy car, and his mother taught him songs of girlish yearning. That photogenic youthful face of his was boyishly pretty, like his singing voice, which was often mistaken for a woman's or derided as ''fey'' and ''effete.'' Even in his final years, when the fashion photographer Bruce Weber made the documentary ''Let's Get Lost,'' Baker seemed to have taken on the mystique of a tragic gay icon, a jazz Camille.