“The Iceman” is now playing at Point and Eastgate Cinemas. R, 1 hour 46 minutes, three stars out of four.

There isn’t a character that Michael Shannon has played that it seems like a good idea to screw with. Even one of his most likable recent characters, the loopy uncle in “Mud,” seemed like trouble.

So it’s something to say that Richard Kuklinski, the hitman Shannon plays in Ariel Vromen’s fact-based crime drama “The Iceman,” is one of his most fearsome characters. The post-title cards say that Kuklinski is thought to have killed over 100 people in the ’70s and ’80s, and in looking into Shannon’s cold, dead eyes, you wonder if that’s lowballing it.

Kuklinski led a double life, both as a busy employee of the mob in New Jersey and as a loving husband and family man. We get a sense of that duality in the movie’s opening scene. In the first, he sweet-talks his future wife (Winona Ryder) on their first date; in the second, he slashes the throat of somebody who insults her in a pool hall.

Once local crime boss Roy DeMeo (Ray Liotta) catches wind of Kuklinski’s “aptitude,” he brings him in as a contract killer. The film follows Kuklinski’s 20-year career, shooting, stabbing, poisoning a long list of victims. He approaches every job with a businesslike precision, his face betraying only a slight irritation at the the pleadings of his victims, like he’s remembering he forgot to pay the water bill. When one victim (James Franco in a cameo) prays for God to save him, Kuklinski sneers. “I don’t feel anything,” he says. “God must be busy.”

The case is peppered with good supporting work from actors who we both expect to see in a mob drama (Liotta, Robert Davi) and some we don’t, including David Schwimmer as a sad-mustached, jumpsuit-wearing rival hitman, and Chris Evans (“Captain America”), almost unrecognizable under scraggly facial hair as a freelance hitman who Kuklinski partners with.

Although “The Iceman” has a high body count, Vromen doesn’t wallow in the blood, focusing more on the characters than the violence they do. There’s no honor or nobility in this rogues’ gallery, just a parade of sociopaths and opportunists feeding on the innocent, and eventually each other. I don’t know that we root for Kuklinski to survive them, but we’re undeniably fascinated at his ability to do so.

We know the arc of “The Iceman” from “Goodfellas” and a hundred other mob movies. Things are good for a while, and Kuklinski is able to keep his life compartmentalized. But the syndicate starts to crumble, with the police closing in and mobsters plotting to whack each other before they get whacked first. The pressure starts getting to Kuklinski, most notably when DeMeo shows up at his daughter’s 16th birthday party.

It’s a testament to Shannon’s raw, gritty performance that even though we’ve seen him kill dozens of helpless people up until this point, we still feel for him a little as his family starts to see him for who he really is. Shannon could have gone for a much more showy performance, but he keeps Kuklinski largely reined in, the fury that occasionally ignites in his eyes more than enough to chill us. He’s not a psychopath, he tells himself. He’s a guy doing a job he seems frighteningly well-suited for.