This is an iffy suggestion, as I've only read one book so far, but Jim Butcher's Dresden Files series is definitely more in the "supernatural detective" vein. Just in the first book, Storm Front, we are introduced to Harry Dresden, a very down-to-earth detective who doesn't like trouble, has few friends (or at least people he trusts), and...is a wizard.
Harry Dresden's being a wizard isn't "too convenient" as far as his skills and abilities go; he has rules he has to obey (or else face grim punishments), and what's more, he doesn't have a spell for every occasion. If, for instance, he doesn't have a certain potion conveniently already made and on his person, he can't just disappear in the middle of a fight; he's HUMAN, very much so...just a human with the right kind of knowledge for how to tap into powers the rest of us tend not to be able to.
The setting is kind of like the Sookie Stackhouse novels in that it's a version of our world, but "used" to the knowledge of various supernatural presences existing alongside the rest of us mugg-- um, less-talented people.
So, when he gets called in by the police to investigate a grisly double-murder, he smells black magic. And just like Jack, he has a smaller, subplot-situated case he's investigating with a woman's missing husband, although there may be more than meets they eye going on with that, as well.
It's all told in first person, and as I said, it takes place in a world that's aware of the supernatural at work, but otherwise, the tone, the building tension, the mystery, the clients - it's all very Jack-like.
And best of all - there's 12 novels and counting! (Along with a forthcoming 13th book and a short story collection.)
So there's my two cents. If you like the RJ series, you're probably going to love the Dresden Files.
"...and your last thought is that you have become a noise...a thin, nameless noise among all these others...howling in the empty dark room"
--Ulver, "Nowhere/Catastrophe"