Cordelia Gray was a detective PD James wrote about in the 70s and early 80s. James seemed to be experimenting with breaking away from her elegant, self-contained series detective Dalgliesh (though Dalgliesh plays a bit part in the first Cordelia Gray book).
But it never worked out. James wrote two Cordelia Gray books, An Unsuitable Job for a Woman, and the much longer The Skull Beneath the Skin. It must have seemed like a good idea, creating a young, spunky woman with a detective agency mostly specializing in lost pets, who gets involved in murder.
James's heart never really seemed to be in it. She discovered that a private eye has few resources for actually solving crimes. Much of the post-murder part of Skull is told from the point of view of cops (anonymous, though extensively described), though Cordelia is eventually the one to figure out who the killer is. James was a professional administrator and bureaucrat, and her heart is with systems. Dalgliesh is a man of system. Cordelia was on her own, and, in the end, I don't think James could come up with plots that worked with that situation.
The stress shows in Skull. All the characters are more schematic than James's usual, despite the length of the book. It lacks the easy charm of the first Cordelia book, Unsuitable Job.
Plus, Cordelia was kind of Dalgliesh's little sister (though there were hints of a potential romance betweent them). She had the same self-sufficient personality, the same literary education, the same cool attractiveness. James hadn't really traveled very far, and so decided to just go with Dalgliesh, the original model.
Sometimes, as a writer, you try to break free, only to find that your restrictions are also your strengths.
I miss Cordelia, though. Maybe because I can't work up a crush on the dark-and-literary Dalgliesh, but have no problem doing so for the catlike Cordelia.