In “Think of a Number,” his first thriller, published last year, John Verdon established himself as a subtle and inventive puzzle master. The novel’s slick “impossible crime,” featuring a serial killer who seemed able to read the minds of potential victims, would have brought credit to Agatha Christie. In the opening pages of “Shut Your Eyes Tight,” Verdon’s taut and suspenseful follow-up, the author appears to be taking us in a different direction.

“Spoiled little rich girl marries hotshot celebrity psychiatrist,” runs one character’s summary. “An hour later at the wedding reception on the psychiatrist’s fancy estate, his demented gardener decapitates her with a machete and escapes.” This time, it seems, we’re in for Grand Guignol.

At first glance, there appears to be little about this short, sharp shock to draw the attention of Dave Gurney, also the hero of Verdon’s previous book. Gurney, “the most highly decorated detective in the history of the NYPD,” has now retired to a quiet farm in the Catskills, attempting to occupy himself with the gentle pleasures of asparagus farming.

His old colleague Jack Hardwick, whose abrasive manner masks a keen insight, suspects that Gurney isn’t quite ready to leave police work behind. “You’re a natural-born onion-peeler,” Hardwick says, “the best that ever was.” Though the case of the “butchered bride” appears to be a simple, if horrific, crime of passion, Hardwick is convinced that the official investigation has wandered off track and persuades a reluctant Gurney to make inquiries.

Gurney soon makes a series of troubling discoveries. It emerges that the chief suspect, the missing gardener, somehow managed to pass in front of several video cameras without being recorded. Stranger still, Gurney concludes that the murder weapon, found dripping with the victim’s blood, was somehow planted in the nearby woods before the crime took place.

’Shut Your Eyes Tight: A Novel’ by John Verdon (Crown. 509 pp. $24) (Crown)

Worse, it gradually becomes clear that the murdered woman may not be the only casualty. Several young women have gone missing from the high-priced academy run by the groom — “a disheartening repository for sex addicts and sociopaths” — each one vanishing after a near-identical argument with her parents.

As Gurney draws these disparate strands of the mystery together, his elusive quarry outmaneuvers him to humiliating effect, leaving the detective’s confidence shaken and his reputation in peril. “No bone shatters as painfully as the illusion of invulnerability,” Verdon observes.

Meanwhile, Gurney’s marriage, already strained by the events of the previous novel, faces a fresh test as his obsession with the case deepens. “I know that what you do takes great strength, great courage, great honesty, and a superb mind,” his wife tells him. “But you know what? I’d like to be a little less in awe of you and a little more with you.” Soon enough, when a grim totem of the murder appears on Gurney’s doorstep, the detective faces a life-changing decision.

Verdon is in top form as he lays out the twisty mechanics of the crime, creating an agreeably sinister villain who caters to “the sickest men on earth.” The author also gives a convincing urgency to his hero’s personal dilemmas, creating a compelling portrait of a marriage unexpectedly tipped into crisis.

For all of Verdon’s many strengths, however, he occasionally falls back on the tired conventions of the thriller genre to gin up suspense. At regular intervals we’re confronted with a page or so of perfunctory ravings from the killer’s point of view, and a late influx of hyper-violent gangsters feels a bit off-the-rack.

In the end, Verdon’s ingenious plotting far outweighs his occasional excesses. “Shut Your Eyes Tight” is a strong follow-up to the author’s wildly entertaining debut. One suspects that Gurney’s asparagus patch will continue to be neglected for some time to come.

Stashower’s most recent book is “The Beautiful Cigar Girl.”

SHUT YOUR EYES TIGHT

By John Verdon

Crown. 509 pp. $24