The compositions of Tim Berne frequently unfurl like spaghetti westerns. There is often an epic choreography of menacing tension and violent eruptions, accompanied by the musical equivalent of sagebrush blowing across a dusty landscape, tight close-ups of hard-bitten hombres and interludes of feisty vulnerability and voluptuous beauty.

Indeed, Berne is most comfortable as a jazz renegade. Though the renowned alto saxophonist recently turned 60 and was named No. 7 among “New York City’s top 25 essential jazz icons” by Time Out New York, he rejects the notion that he has become an influential elder statesman.

“Everybody thinks I am an adult now,” he said sardonically by phone from New York. “I’ve been doing this for 40 years.”

Berne, who will bring his group Snakeoil to Minneapolis’ Icehouse on Monday, didn’t purchase his first alto until he was in college, and wasn’t inspired by jazz until he heard the soulful blues and grit invested in the genre by saxophonist Julius Hemphill.

By age 27, he had moved to New York to study with Hemphill and self-released three albums. By his 30s, he was recording for Columbia Records, a major-label relationship that was destined to fail given the uncompromising, freewheeling tenor of his music. Since then, he has recorded dozens of discs for a variety of labels, but primarily his own imprint, Screwgun.

Against that backdrop, his work with Snakeoil is a bastion of slow-building stability in the Berne canon. The core quartet has been playing together for six years, and has released three albums since 2012 on the prestigious ECM label. His writing for the group has become increasingly elliptical and serpentine, while the interplay is at once more taut and daring.

Dismissing an ECM press release that praised his maturity as a songwriter, he commented, “It isn’t that the writing is more mature. It is that thousands are hearing it instead of hundreds. Let’s face it, when I was on Columbia, people were impressed mostly because it was on Columbia.”

Point taken. In the 1990s Berne helmed another remarkable ensemble, Bloodcount, that released six albums over a three-year period. But all those discs were live recordings, without the pristine acoustics for which ECM is renowned.

Giving them ‘a lot of rope’

As Berne describes the songs on the third Snakeoil album, “You’ve Been Watching Me,” released last month, it is easy to glean that this has become a special band.

“I give these guys a lot of rope,” he says, referring to original members Matt Mitchell on keyboards, Ches Smith on drums and vibes, and Oscar Noriega on clarinets, as well as newcomer Ryan Ferreira on guitar. (Ferreira won’t be at the Icehouse gig.)

“I might say, ‘After the theme it will be clarinet, guitar and drums, and when I come in people can stay in and make the contrast.’ On this record we exploit a lot of different combinations.

“There are maybe five or six versions of what will happen in my head. It is a timing thing. You can’t be thinking solo-istically instead of dramatically when you push ahead. You want contrasts and different kinds of gymnastics. It is like a relay race — the last one is the one who ends the race. You can’t have the race end four times.”

Noriega puts it a little differently. “The recent pieces are less through-composed because he feels we know the music better. What I love about Tim is you play his music correctly but he never tells you how to play; he lets you figure out your role. You can kind of feel what people are thinking now: If somebody shifts, everybody shifts along with it. I think of it as a huge canvas that is constantly changing.”

Over the years, Berne has frequently deployed longtime friend, guitarist and occasional bandmate David Torn as his producer. “David is a master of pulling up the subtle details, getting the most out of the music,” he says.

To hear Torn gush about Snakeoil, there is a surfeit of details to highlight.

“You have this composer with a huge ear for possibility. He’s working with a band he knows very well, allowing his compositions to not only absorb improvisation, but inspire it. That is a remarkable thing, an organic thing, and Tim’s positive energy is moving it forward. It is a loaded word, but I think that is genius.”

At the heart of Snakeoil’s serpentine lubrication is Berne the composer, but Berne the saxophonist is integral to the elixir. “You hear that alto and you know within two notes it is Tim,” says Noriega. “When we first started playing it was mostly duets and there was a special timbre. He is very dynamic, never boring. He needs to keep it fresh. Now we have about four sets of music we can play and we never play the same set list twice.”