In the past 30 years or so, as crime fiction has advanced from the paperback racks to the hardback bestseller lists, more and more talent has been drawn to the genre, and this has led to more and more innovation. These days, many of the novels that come my way fall, much like today’s movies, in two categories: the blockbusters and the smaller-scale tales that are the novelistic equivalent of indie movies.

I’ve had the good fortune to review some excellent blockbusters recently — notably John Grisham’s “Sycamore Row” and Robert Harris’s “An Officer and a Spy” — but I’ve been just as happy to welcome offbeat works such as the recent “Girl With a Clock for a Heart” and “The Last Dead Girl.” Such novels are usually too quirky to climb the bestseller lists, but they can delight readers who enjoy stories that are variously wry, unexpected and perverse.

This week’s “Love Story, with Murders” is a good example. It’s essentially a police procedural that features 26-year-old Detective Constable Fiona “Fi” Griffiths of Cardiff, Wales. Fiona was introduced in “Talking to the Dead” (2012), and this time she’s confronted with two bodies that were chopped into small pieces and scattered around an otherwise comfortable Cardiff suburb. (Her colleagues, afflicted with deplorable police humor, call the case Operation Stirfry.) The search for the killer (or killers) leads to some respectable citizens who are up to no good, and also pits Fiona against a pair of sadistic hit men. It’s a perfectly okay plot, but that isn’t what makes the novel fun and even memorable.

That would be Fiona herself, who’s one of the more improbable but, in her own way, endearing cops I’ve ever come across. To start with, she doesn’t know who her birth parents were, because at age 2 she was left in the back seat of a car owned by a man named Tom Griffiths. He and his wife became loving parents to Fiona, although Tom was the biggest crime boss in Wales.

Despite an apparently happy childhood, Fiona suffered a major breakdown as teenager: “I was ill for two years. Mental illness, as bad as it gets. For much of that time I was kept in a secure unit.” She was suicidal, “a girl who couldn’t feel herself existing.” She doesn’t know what caused her condition. Perhaps trauma in her early life. She’s still seeking the truth of her past.

”Love Story, With Murders” by Harry Bingham. (Delacorte)

For all her problems, Fiona is an excellent cop. She’s smart and dedicated and fearless — often too fearless — and she has a sixth sense that often leads her to answers others don’t see. It helps that she communicates with the dead, or at least thinks she does. She also partakes of homegrown marijuana to help steady her nerves. She is, in short, not your run-of-the-mill cop: “I’ve never thought I would plant my flag permanently on Planet Normal. This planet is not my own.”

The love story of the title involves Fiona’s boyfriend, a fellow cop named Buzz, who helps keep her semi-normal. Buzz is a hunk, and she’s determined to be the perfect girlfriend, which contributes to their active, possibly therapeutic sex life. On the down side, Buzz is such a straight arrow that she’s afraid he might arrest her if he finds the plants in her potting shed. She agonizes about the pros and cons of marrying Buzz.

A turning point comes when Fiona and other cops are searching a neighborhood where body parts were found. She enters a backyard shed and thinks things over. “I realized I’ve been searching the wrong way. . . . The police way, not mine. As though corpses had nothing to say to me. . . . If I had a joint with me I’d smoke it now.”

She notices a plastic barrel, filled with old motor oil. She hears laughter, the kind no else can hear. “I share the joke until the silence grows too strong, then kneel down by the barrel and thrust both hands in. They come out with Mary Langton’s blond and dripping head.”

To complicate matters, Mary Langton turns out to have been a pole dancer in one of Fiona’s father’s nightclubs. Such surprises keep “Love Story, with Murders” spinning along. If I have a complaint, it comes when two thugs capture and intend to kill her, but by luck and pluck she survives. Such miracles are basic to the genre, of course, but what really matters in this novel is the sweet, strange complexities of Fiona’s mind. “Love Story, with Murders ” is a dark delight, and I look forward to Fiona’s future struggles with criminals, her demons and the mysteries of her past.

Anderson regularly reviews mysteries and thrillers for Book World.