If they gave Emmys to the actor who most aggressively avoided stereotyping, Michelle Dockery (top) could be writing her acceptance speech right now.

Dockery’s Letty Raines character in Good Behavior, a new TNT drama that premieres Tuesday at 9 p.m. ET, takes her several galaxies away from Lady Mary Crawley, whom Dockery played on the late lamented Downton Abbey.

Unless you can picture Lady Mary sitting in her underwear on the side of her bed in a cheap motel, snorting drugs and contemplating whether to kill herself over a wasted life that included multiple criminal activities, a prison term, and an abandoned 10-year-old son.

Mild spoiler here: Letty doesn’t kill herself. She meets a fella named Javier (Juan Diego Botto, left), albeit in a rather dicey and extra-legal situation. From there Good Behavior spools out as a combination of a dark action-adventure crime thriller and an unlikely romantic dance between Letty and Javier.

And did we mention that Javier is a hitman? Yup, he kills people for a living.

They say there’s someone for everyone.

Now all this could easily turn into a plate of bad hash, a B-movie rewarming of Bonnie and Clyde and No Country for Old Men with a little Breaking Bad on the side.

But Good Behavior pulls off the mashup well, at least in the early episodes.

The show also takes a rather sharp turn between the first and second episodes, which will be easy for viewers to spot because those first two will air back-to-back on opening night.

The first episode lays out Letty’s bleak situation. She’s just out of prison and trying to kick her drug habit while she figures out some way to earn money other than theft.   

Her parole officer Christian (Terry Kinney) is breathing down her neck, and she can’t persuade her mother Estelle (Lusia Strus, left) to let her see her son, in whose care she left the lad while she was doing hard time.

Mom, no gem herself, is convinced Letty is a bad influence.

By random chance, Letty overhears Javier taking a gig to kill a woman who has become inconvenient to her husband. She decides to see if she can intervene and stop it, which leads her into a series of events that swing from awful to oddly exhilarating. And back.

In the second episode, Letty’s situation isn’t much better nor are her results. But we’re starting to see a downshift in the prominence of the weekly crime dramas, as the focal point shifts to Letty and Javier.

Those weekly dramas are essential, and they can get pretty intense. But the long game here is what goes on, or sometimes doesn’t go on, in the relationship.

That’s a good decision for keeping viewers interested because the relationship becomes our window to everything else about the characters. It’s also what has the potential to set Good Behavior apart from your average crime procedural.

Dockery plays Letty intensely and well, convincing us this street-hardened, often calculating woman has a wide streak of vulnerability that she rarely dares to reveal.

Botto, in the same vein, humanizes Javier without pretending that his chosen line of work is socially and morally acceptable.  

Good Behavior, which is based on Blake Crouch’s Letty Dobesh stories, exemplifies the kind of edgy show toward which Turner’s new entertainment chief Kevin Reilly is moving his networks.

It’s a gamble since he has jettisoned some really good dramas he inherited, like Rizzoli & Isles. But if the replacement shows could all be this good, he just might find that new niche he’s after.