Named after the recently-turned-80 singer-songwriter from Texas, Willie Nelson, the Little Willies, in the spirit of their namesake, play country music their way.

The group’s second album, For the Good Times, includes classics written and/or performed by Nelson, Hank Williams, Johnny Cash, Loretta Lynn, Dolly Parton, Lefty Frizzell, Kris Kristofferson and Ray Price.

“Ninety percent of the time, we’re not trying to be authentically country,” said singer-guitarist Richard Julian, a member of this band of friends that includes singer-pianist Norah Jones. “It’s more about the essence of the tune, the story of the song and the melody. If anything, we want to demonstrate the songs in another environment and show how well they work.”

Nelson, of course, is a multi-genre-spanning musician who won’t be bound by a country tag.

“He’s one of my favorite musicians,” Julian said from his home in Brooklyn. “And everyone in the band will say that. Willie is just one of those guys who is never afraid to be himself. He’s called ‘country music,’ but he’s just playing his stuff, singing behind the beat, ahead of the beat, and ripping the guitar solos. He’s a force of nature.”

The Little Willies made their debut in 2002 at a tiny New York City venue, The Living Room. Julian wasn’t part of the group then but Jones, with whom he’d recorded a song for a Waylon Jennings tribute album two weeks before, invited him to come along and perform the Jennings song “Wurlitzer Prize.”

Julian had known before the latter show that Jones liked some country music. She’d been mightily impressed, he recalled, that he’d known the late, tragic Texas songwriter Townes Van Zandt. But Julian had never experienced the more extroverted side of Jones’ music making. He heard that for the first time at The Living Room when she rocked country classics at the piano with the Little Willies.

By the time the next Little Willies gig rolled around, Julian was in the band. The original plan for the group was to play Nelson songs exclusively.

“But nobody had the time to apply themselves to learning all the Willie tunes, so we ended up just doing tunes that we knew,” he recalled. “The next thing you know we were into this alter ego of our musicality, which was really great, very natural.”

The same year that the Little Willies played their first show, Jones’ career exploded with the February 2002 release of her solo debut, Come Away with Me. An international success, the album won eight Grammy awards and sold 25 million copies.

Once the stardust from Jones’ sudden fame settled, the Little Willies regrouped and released their self-titled album debut in 2006. It includes Van Zandt’s “No Place to Fall,” Fred Rose’s “Roly Poly,” Jerry Leiber and Mike Stoller’s early Elvis Presleyhit “Love Me,” and a lesser known Nelson song, “I Gotta Get Drunk.”

“Those songs are so well crafted,” Julian said. “It’s inspiring, really. I love songs, I love songwriting.”

When the Little Willies make their New Orleans debut Saturday at the New Orleans Jazz and Heritage Festival, it’ll be a homecoming for Julian. He lived in the city’s Bywater neighborhood for two years before returning to New York.

“I want to go back to New Orleans,” he said. “I have a great scene here in New York, and I’ve been established here for a long time, but it’s so hectic. New Orleans was better for me as a writer. And I love playing a piano out by the window and having people yelling into the house. I just dig it. It was really a beautiful experience.”