Isaac Asimov once said that writing a mystery is simple: Devise a situation that can be explained in more than one way, build a case for one of those ways, and at the end, reveal the "truth" to be different.

Simple, perhaps, but not easy, because each scenario, especially the feint, has to be believable, or there's no sale. Therein lies the difficulty in Boston writer Dennis Lehane's fourth novel. Lehane is clever with words and can paint a good scene, but too often in "Gone, Baby, Gone," the reader is left with the sense that it wouldn't have gone that way.

When private detectives Angie Gennaro and Patrick Kenzie want to review every local TV station's coverage of the kidnapping they have just agreed to investigate, for example, they ring up a guy Angie dated at New England Cable News, and he sends tapes by overnight express. Not just NECN's tape, but all eight stations'. He just had them. "Don't ask me how he pulled this off," narrator Kenzie says, anticipating the obvious question -- but, well, how else are they going to get their first lead?

Amanda McCready is the girl who has been kidnapped, snatched from her bed one night while her mother is over at a friend's watching television. It's the highest-profile case around here since the abortion-clinic shootings: vows from the mayor, bulletins every hour, squads of police pulling overtime trying to rescue the 4-year- old.

Despite such intense investigating, Amanda's aunt and uncle come to Kenzie and Gennaro, undeterred by the detectives' "pretty steep rates," even though Uncle Lionel's just a blue-collar guy delivering for UPS and living in Dorchester. The private eyes are reluctant, not wanting to bankrupt them and not wanting to find a dead child.

While deliberating, they encounter the cop leading the chase. Ordinarily, as any mystery reader knows, the police despise meddling by outsiders, especially private detectives, but this one's different. He not only registers merely the mildest of objections, he assigns a couple of liaison officers. (They'll come to you, he tells our heroes!) From then on, Kenzie and Gennaro function as if on the force, brandishing their guns, holding discovered loot in their own private evidence lockup, even conducting an illegal black-bag operation with police involvement. Yeah right, you might think -- but, well, how else will they, and the reader, keep up with the case?

Such questions keep arising, and they're particularly disappointing because "Gone, Baby, Gone" is otherwise delightful reading. Lehane describes a leading bad guy, for example, as a freak of nurture. And when a policeman removes a stick of gum from itsfoil wrapper, the sound is "like teeth on my spine," a fresh allusion that elicits a shudder.

Lehane is adept not only at describing situations but at creating them. It's amusing to see Amanda's mother plop down in front of the TV at a crime scene, zoning out to Jerry Springer while two victims of the drug trade rot away in the next room. Just outside, a neighbor is beating a rug with the shaft of a hockey stick, its blade no longer attached. The image has the feel of Charlestown, exemplifying Lehane's thorough grasp of his backdrop.

Insider references abound, such as when Kenzie, while bragging about the Old Colony housing project in Southie, mentions its teen- suicide problem. A local cop justifies not bringing the FBI into the kidnapping because they're such screw-ups, like when they "cut insane deals with the Boston mob." And then there's this pithy offering to the Chamber of Commerce: "Boston: We're small, we're cold, but we'll kill for a good parking space. Come on up. Bring the family."

Such touchstones are fun, even if they sometimes give pause. Lehane, who grew up in Dorchester, says up front in an author's note that he has deliberately taken liberties while describing local particulars. So when the scene shifts to the Granite Rail Quarry in Quincy, for instance, some local readers might ask if that's one of the real places, or one of the made-up ones. (It's real.) And you have to wonder when Lehane refers to John Salvi's abortion-clinic bombings, when practically everyone knows he used a rifle.

If your disbelief is easily suspended, there's enough in "Gone, Baby, Gone" to warrant staying up late with it on a summer's evening. Ultimately, though, the mystery of a mystery ought to be in the story, not in why the author thought the story was believable.