I’ll also recommend Andrew Vachss’ Burke series, though I’m not sure how obscure it is.
For something obscure, but less literary, there’s PN Elrod’s “The Vampire Files” series. The main character is a slightly Kent Clark-ish former newspaper reporter, turned vampire, and his best friend a British stage actor, with a good eye for deduction. They’re fun.
(Yeah, what’s that all about??? The hero is a proper gentleman but never made a single comment about anyone else’s sexual behavior. And his boss is a lesbian, and he greatly admires her.)
Dalziel and Pascoe series by Reginald Hill is often excrutiatingly funny, I’m sorry there will be no more. (they have been around for a long time, Pascoe’s wife was originally written as a raging wimmens libber. I wonder if she still was, toward the end of the series.)
Not at all obscure in the least, Ruth Rendell/Barbara Vine has recently suffered a stroke. 
Her work, her mystery series alone, is in a class all by itself, at the very top of the heap.
Speaking of Singapore, Bangkok-based American writer Jake Needham has started a decent series set in Singapore featuring Inspector Samuel Tay.
Needham also has some other mysteries that could conceivably be counted as a series, although they’re mostly two-offs or just happen to contain a couple of characters from other books.
I was going to mention the New Orleans homicide detective La Stanza by O’Neil de Noux. I liked them so well I still own the battered paperbacks of the first three from the '80’s. Since they were released new in paperback, and in the ‘support local authors’ bookstore section, and only my New Orleans ever heard of them I thought they were obscure. So I googled the author and he’s way famous. :o New books! New series! What a fool I was to lose track of him. But on the other hand, NEW BOOKS! Whoo hoo!
Damn, you guys are bringing tears to my eyes. Back when I was in mystery publishing (roughly 1985-2002), I edited a lot of these guys – Marshall, Westlake, Ellroy, McBain, Kaminsky – and knew most of the rest of 'em. Bill Marshall is a terribly amusing drunk, by the way.
Ever read Jonathan Latimer? His hardboiled PI novels featuring Bill Crane are excellent. And SOLOMON’S VINEYARD is legendary. He also wrote the screenplay for THE BIG CLOCK (1948), with Ray Milland & Charles Laughton, which every noir/thriller movie fan should have on their to-watch list.
Ah hell. This is too soon after PD James’ death. I started out reading just her Wexford mysteries because I didn’t like the psychological suspense ones and then a few years ago, it was like switching on a lightbulb and now I can’t read them fast enough.
Peter Dickinson wrote quite a few literate mysteries in the 70s and 80s. I don’t think he’s very well known in the US. I see he’s 87 now. Maybe I should write him a fan letter soon.
I could be exaggerating about this issue (it’s a long time since I last read anything by Burke). Possibly, indeed, it was only one reference in one novel (no idea now, which one) – but I honestly don’t think I dreamed it. And maybe just a trait given by the author to Robicheaux, rather than Burke’s own opinion; but I recall Robicheaux suddenly expressing himself very strongly against that particular practice (interior monologue IIRC, and not about any particular character). My thoughts were, “Wow – where did that come from; and what makes him so extremely vehement about it?” From what I recall, it’s not that he believes that you’ll be sent to hell for doing this thing – he just finds it infinitely contemptible.
I’d forgotten all about the lesbian boss. If he’d been on her case about that, most likely I’d have remembered: further evidence, I’d reckon, that Robicheaux’s sentiments are not from conservative religious belief – otherwise he’d probably have had a problem with the boss’s lesbian-ness, even if respecting her professional competence.
Yes, I burned out on Burke at least ten years ago. Same with J.A. Jance. I just don’t enjoy detectives “in recovery.”
I liked much of the Blind Justice series by Bruce Alexander (RIP). It was well-conceived, being both historical fiction and mystery and featuring Sir John Fielding who really was a blind magistrate in 18th Century London who really was the brother of the writer of Tom Jones, Henry Fielding.
The later books become pretty formulaic. I think Bruce Alexander who created the series was getting a little long in the tooth but still being told to crank out fiction. Mystery fans are so voracious and fickle that if they don’t have a new episode every year they are on to the next hot thing. And when the prose suffers because it has been milled unevenly, we blame the writer and move on to the next hot thing.
A viscous circle.
Peter Corris - Cliff Hardy series set in Australia
Peter Temple - Jack Irish series set in Australia.
Jussi Adler-Olsen - Carl Morck department Q series set in Denmark
Karen Fossum - Inspector Sejer series set in Norway
Peter Robinson - DI Banks series set in Yorkshire
Arnaldur Indridason - Inspector Erlander series set in Iceland
Try one and if you like it, rest assured the rest of the series are equally good.
Dan Kavanagh wrote four books centred on Duffy, a shortish London ex-cop. Duffy was a hypochondriac, not very good at running a business and bisexual at the start of the emergence of HIV.
The books are a delight. They have just been reissued over the past year, after circulating like hot Picassos in the underworld. I give them three chefs hats.
Also, since you started with an Australian setting, I’d second recommending Peter Temple’s books. Set in contemporary Australia, there are two loose series - one based on Jack Irish and the other on a network of detectives in The Broken Shore and Truth.
Gary Disher produced a series based around the adventures of Wyatt, an old style crim, which are outstanding and has a new series set on the Mornington Peninsula focussed around several police stations. Again, really good stuff, perhaps not as edgy as Temple in subject matter or character, but both very evocative of the setting.
Maybe he really was choking a python. Not everything has to be a metaphor.
Barabara Nadel’s Inspector Ikmen series, set in modern Istanbul. First one Belshazzar’s Daughter
Kate Ross’ Julian Kestrel series. Only four in the series, alas, because Kate Ross died. A Broken Vessel is the first one.
Sara Gran’s Claire Dewitt series. Do only two books make a series? These are present day, fringe of hipsterdom noir, replete with Jungian references and Buddhist philosophy and lots of drugs and booze. Suffering, cruelty, redemption. All much more intelligent and original and better than I’m making it sound. Claire DeWitt and the City of the Dead is the first one, and the follow up is Claire DeWitt and the Bohemian Highway.
Is Lisa Lutz’s Spellman Files series too well known to mention? They made me laugh out loud. A lot.
I really enjoyed the Grift Sense series by James Swain, featuring Tony Valentine, a retired cop who sets up a business as a consultant to casinos as his specialty is exposing cheats.
Was ‘The Nameless Detective’ by Bill Pronzini mentioned? Because there are quite a few entries in this old fashioned series set in San Francisco.
I was coming in to mention Kate Ross, whose books are just lovely, and such a shame.
But … nitpick … Cut To The Quick is first, though A Broken Vessel is a perfectly acceptable starting point and, IMO, a better book.