Crime fiction round-up: An elephant, a mystery baby and a suicidal detective

Of all popular fiction genres, crime might at first glance seem to be one of the most circumscribed – after all, there are certain key elements that must inevitably be present (tenacious detective, plot revelations at crucial points, the denouement). But look at some of the most intriguing entries in the current crime crop and you'll see just how wide the field can be and how different the various books.

Let's start with a blockbuster American thriller, and a keen reminder of the pleasures afforded by such top US writers as Linwood Barclay. Broken Promise (Orion, £18.99) is a treat, full of ingenuity and flair and, what's more, it's a book that does not accentuate its effects, but assumes that the reader will be paying the closest attention.

As ever, Barclay trades in Hitchcockian suspense, his reporter protagonist David Harwood struggling with both redundancy and single parenthood in smalltown America, where everyone knows everyone else. Things go drastically wrong when David visits a cousin who is looking after a baby who, she says, was "delivered to her by an angel". But across town, a mother has been stabbed to death…

We are taken to a very different milieu by the British writer Ann Cleeves, whose latest book featuring her shambolic copper Vera Stanhope is The Moth Catcher (Macmillan, £16.99), with Vera investigating the death of an ecologist. As so often with Cleeves, we see her take an idea and work it out with ingenuity; everything is told crisply in scenes full of sharply observed detail.

Back to the US, but in the company of another Brit, and another contrast: Make Me by Lee Child (Bantam Press, £20) is typically blunt and energetic stuff, with Jack Reacher investigating a mystery involving the death of 200 people in another minatory prairie town. Child hates literary snobbishness and delivers popular writing that grips the attention thanks to some subtle adjusting of his narrative methods. The very fact that this is formulaic fare allows him to add precisely judged, subtle twists to what we've come to expect.

I have mentioned the wide range of current crime fiction, and the title of The Unexpected Inheritance of Inspector Chopra by Vaseem Khan (Mulholland, £12.99) tips the wink that this is nothing like the other books in this column. The eponymous Mumbai inspector (with the aid of a trusty elephant) tackles crime in a narrative that owes more than a little to Alexander McCall Smith.

Talking to many of the practitioners of Nordic noir, I have found one female character mentioned again and again as an influence, so there will probably be healthy sales in Scandinavia for Tennison by Lynda La Plante (Simon & Schuster, £20), in which Jane Tennison's creator presents her as a young WPC, already struggling on a first murder case. It may be apprentice Tennison, but it's vintage La Plante.

Still in search of something different? Try a brace of impressive foreign entries: Jussi Adler-Olsen's The Hanging Girl (Quercus, £16.99) is more Department Q skulduggery, weighing in at a massive 600 pages, with reluctant Danish detective Carl Mørck and his intuitive Muslim assistant, Assad. It's mesmerising writing from Adler-Olsen, with an added level of mystery – who is the uncredited translator?

Finally, more evidence that French crime is in rude health: the first book by multi-award-winning Michel Bussi to be translated into English is After the Crash (Weidenfeld, £7.99, trans. Sam Taylor). This is something unusual: a crash on the Franco-Swiss border kills all the passengers on a plane apart from a three-month-old baby girl. Two families step forward to claim her, but it's two decades later before we learn her identity. With its suicidal detective, it's safe to say readers won't have encountered anything quite like this one before.