The narrator-hero of Roberts' first mystery novel is a semi-successful L.A. actor and part-time sleuth called Saxon--no first name, just Saxon. And this coy, overused mannerism is just one of the clichÃ‰s and hollow borrowings that mar an otherwise promising debut. (Winner of a ""first private eye novel"" contest sponsored by St. Martin's, Macmillan Ltd. in London, and the Private Eye Writers of America.) Saxon, hired to figure out who's trying to kill veteran novelist Buck Weldon (a bullets-and-blonde Spillane type), has reason to suspect Weldon's vengeful ex-son-in-law (a washed-up football star), his wild younger daughter (into the cocaine scene), his semi-shady publisher, even his seemingly loyal agent. But the likeliest motive would seem to involve Weldon's newest book, still-in-progress: a roman Ã clef about a recent Hollywood-studio scandal (which Roberts unimaginatively models on the Begelman affair). So the sleuthing and the rough stuff center largely on foul studio-head Mandelker--and his violent henchmen--until the Big Secret of Buck Weldon's life (heavily hinted at throughout) is revealed in a scenic Baja showdown with the implausibly motivated killer. Saxon's smug, ironic narration is often blatantly derivative (""My head was pounding like a Louis Bellson solo""); his love-at-first-sight romance with Weldon's older daughter is unconvincing gush, especially when it involves amateurish stretches of stream-of-consciousness sex-prose. But there's enough brightness here--brisk dialogue, lean action, varied L.A. backgrounds--to suggest better things ahead.