Getting the three women of Puss n Boots on the phone at the same time creates the kind of chatty camaraderie that graced the stages of little New York clubs long before the rootsy trio made an album and drew a wider buzz as Norah Jones’ new band.

“That’s part of the reason why the last eight years of playing in this band have been so fun,” says Jones, who set aside her piano—and established solo career—to play electric guitar and fiddle within the countrified kinship of Puss n Boots.

“I never get to work in an all-girl band,” injects fellow singer/songwriter Sasha Dobson. “I’ve spent my entire life singing with jazz musicians, predominately men. In this band, we egg each other on, support each other and push each other to try new things.”

That’s a boon for Catherine Popper, best known for her high-profile stints as bassist for rockers Ryan Adams, Grace Potter and Jack White (including on his new album Lazaretto). “We were buds,” Popper says of her new gang. “I don’t really have my own project, so it’s been such a learning experience for me to step up and be a singer.”

Jones, who swept the 2003 Grammy Awards with her solo debut Come Away With Me, embraced her own learning curve. “This has been a great place to work on my guitar playing,” she says. “We just played in dive bars till we kinda got our sound together. I don’t even know that we ever thought we’d make an album.”

That’s changed with the release of No Fools, No Fun on July 15 and a short initial tour that brings Puss n Boots to three area gigs: the Green River Festival on July 12, the Sinclair on July 24 and the Newport Folk Festival on July 26.

“We’re doing bigger shows than we’ve ever done with this band,” Jones says the day after the group played the Clearwater Festival by the Hudson River—a show broadcast on the radio. “We were told we weren’t allowed to curse, and this band is usually pretty late-night,” she says. “You never know what these sweet girls are going to say onstage, so I think that threw us off more than anything!”

Because Puss n Boots found its footing in front of audiences, No Fools, No Fun mixes studio originals with live and studio covers, ranging from Rodney Crowell’s “Bull Rider” and Roger Miller’s “Tarnished Angel” to Wilco’s “Jesus, Etc.” Jones even emulates Neil Young with her own dry lead-guitar snarl on “Down by the River” while guitarist Dobson holds down the drum kit. The group recorded the live tracks at its favorite Brooklyn haunt, the Bell House.

“It would be a little weird to have only a studio album for this band,” Jones says. “Our energy live is more on the fun, silly side, and when we recorded a few of the covers [in the studio], they didn’t have the same energy that they do live.”

In addition to switching instruments, the three musicians swap lead and harmony vocals. “Anything with luscious three-part harmonies obviously is an inspiration,” says Popper, who plays acoustic guitar as well as bass. “That’s part of what got us by in the beginning,” Jones adds with a laugh, “when I was f—ing up the guitar all the time. Well, we sang real pretty before we could play all the chords right!”

Indeed, despite the self-deprecating banter, the trio weaves some sublime harmonies. And the originals—two each for Dobson and Popper and one from Jones—balance nicely. Dobson’s vocals charm with smoky resonance, much like Jones’ early work, while Jones sparks breezy honky-tonk in “Don’t Know What It Means” and Popper inspires intriguing harmonies in her spectrally picked “Pines.”

“We have a certain luxury of knowing each other’s sound,” Dobson says. “There’s a comfort level that’s so powerful. I often forget [that] until we start playing.”

Eventually though, Puss n Boots will return to part-time jam sessions. “We’re not going to stop the other things we do,” Jones says,  “but it’s definitely fun to make this the focus for a while.”

Puss n Boots plays the Sinclair on July 24.