Every time a new tortured-cop show turns critics all gushy and trend-chasing television watchers all buzzy, a guy in Wyoming just shrugs and emits a noncommittal grunt. He’s Sheriff Walt Longmire, and if he’s upset that shows like “The Following” and “True Detective” get more attention than his does, he’s not letting on.

Walt is the title character in “Longmire,” which begins its third season on Monday night on A&E. Like certain other cable dramas — “Justified” comes to mind — “Longmire” has had fine acting and intricate writing right from its first episode in June 2012, but it has settled in as a taken-for-granted steady performer rather than a show that electrifies social media and awards panels. (Number of Emmy nominations: none.)

That’s odd, because the series has plenty going for it, led by the performance of Robert Taylor as Walt. He plays the sheriff of a fictional Wyoming county who has a lot to deal with: weird crimes, a nearby Indian community with its own rules, a deputy who wants his job, a 10-gallon-hat full of personal issues and secrets. He does it with few words and a willingness to bend the rules, and Mr. Taylor’s gritty performance reminds us that this archetype owes as much to the cowboy tradition of John Wayne and Clint Eastwood as it does to noir.

Walt struggles to come to grips with the death of his wife. When the series began, it seemed as if cancer had killed her, but over two seasons, we have come to learn that she was murdered, and that the search for the killer continues. Among the cliffhangers last season was the arrest of Walt’s friend Henry Standing Bear (Lou Diamond Phillips) in the case.

Mr. Phillips is terrific, as is the rest of the cast, and the writers have given each character more to do as the series has gone along. Last season, Walt’s top deputy, Branch Connally (Bailey Chase), ran against him for sheriff, but now Branch has more life-threatening things to worry about: In the Season 2 finale, he was shot by a mysterious ghostlike figure while on Indian land. Walt, too, has a life-threatening matter to ponder: His daughter (Cassidy Freeman) was hit by a passing vehicle and nearly killed while changing a tire on Election Day.

Katee Sackhoff plays another deputy, Vic Moretti, whose back story was fleshed out quite a bit in Season 2. Turns out she fled her previous job in Philadelphia after setting off a corruption investigation against a colleague, and now his former partner, her nemesis, has found her in Wyoming.

The writers weave all of this into a crime-of-the-week structure, and those crimes show an addictively twisted taste. A fatal bear attack turns out not to have been an act of nature. A safe-deposit box delivered to Walt contains a severed finger. The show, which is based on the novels of Craig Johnson, mixes elements of Indian heritage and spirituality into this already rich concoction, and the result is consistently engaging and surprising.