The Cuckoo's Calling by Robert Galbraith (aka JK Rowling)

This has the characters and potential to be the lead in a string of series murder mysteries. A bit convoluted, but well managed. The opening is a scene of the death of supermodel Lula Landry. The police investigation submits a verdict of suicide, but the brother of the deceased eventually goes to private detective Cormoran Strike because he is convinced that it was murder.

Took me a while on the title. It seems to be connected to the fact that one of Lula's friends was in the habit of calling her Cuckoo. Each of her friends had a different name for her, it seems. However, that is not the real connection, I think. The cuckoo is best known (after its distinctive call) for its habit of finding a momentarily unattended nest, pitching out the eggs, and laying its own there for another bird to raise. Lula and both of her brothers, one of whom died as a pre-adolescent, were all adopted. The detective, Strike, is the illegitimate son of a much married rock star (perhaps patterned unsympathetically on Mick Jagger) who neglected to marry Strike's mother, an acknowledged supergroupie. A whole collection of potential cuckoos.

I would like to see a second book, if only to see how long it takes competent and concerned no-longer-temp secretary, Robin, to dump her tediously conservative fiance.