The pirates first announced themselves to Rickie Lee Jones in New Orleans, in the fall of 1979, with a delivery of mysterious gifts.

"I checked into my hotel and there was a dress hanging there, and a gift. I opened it up and it was a diamond necklace, an ostentatious diamond necklace," she recalled. "And they sent drugs to all the guys. All the band was very high. And I said, I can't take these gifts ... it was like a dove with three diamonds in it. I would never wear a diamond back then."

Jones was traveling in support of her self-titled debut for Warner Bros., the slinky, imaginative sui generis blend of pop, soul and jazz that had already hit No. 3 on the Billboard 200, landed her on her first Rolling Stone cover, and associated her forever with the beret. In a couple of months, she would win the Grammy for best new artist. She was almost 25.

The pirates, who were actually local marijuana smugglers, came to her concert and introduced themselves, and although she was nonplussed by their extravagant gesture, they eventually became friends. In fact, when she took an apartment on the seedier downtown edge of the French Quarter in the early 1980s — inspired partly by Dr. John, whom she'd met back in Los Angeles — she split the rent with one of them.

"It was the combination of them and Sal Bernardi's crew in San Francisco that inspired the concept of Pirates," she explained. Some of the pirates went to prison and got out. One moved to Costa Rica. One still lives in New Orleans and now, 36 years after the release of Pirates, her second album, so does Jones, although not in the Quarter: Her neighborhood is leafy and quiet, near a park where she can walk her dog and ride her bike, her freshly purple-dyed hair tucked under a helmet.

"To be really clear, I was a drug addict when I lived here," she said. "It's not possible to walk in the footsteps I walked then. I woke up late in the afternoon, and I lived at night." It was a funny thing, really, to take off to the bottom of the U.S. at what seemed like the top of a career and hang around with dope smugglers, aging artists and weird characters — she was there at Professor Longhair's last recording session, she said, and befriended the one-eyed junkie piano genius James Booker, who'd die in 1983, at age 43 — but it felt right to her, "like a refuge," she said.

"For me, it was part of feeding who I was. I felt that if I stopped living that way, whatever it was that I really was would stop being authentic," she said.

New Orleans and its characters helped inspire the cinematic storybook of hip that is Pirates, with its evocative imagery — the '57 Lincolns, the slow trains to Peking, the Lolitas playing dominoes and poker behind their daddy's shacks — as did Olympia, Wash., where she started writing it in 1979, New York City, where she was also paying rent, and L.A., where it was recorded. Close to forty years later, she still plays those songs onstage. Some feel different than others — for example, "We Belong Together," the ecstatic, dreamy stream of consciousness that opens Pirates, inspired by her famous romance and breakup with Tom Waits.

"When I sing that song, to me anyway, it doesn't have anything to do with me. It's like a house I built. When I go in, I say, 'I love this room. I'm gonna sit in this room.' It's a structure of its own and I get to experience the ride when I play it. But it's not about Tom and me. It has a life of its own."

"There are only a couple of songs that haven't achieved autonomy," she said. "And when I sing them, I feel like, 'I don't wear my dress that short anymore."

But 36 years later, Pirates is a dress that's not out of style, a house that still welcomes new residents. It's canon, classic, a still-startlingly singular look at America both in style — the way it seamlessly weaves threads of beatnik jazz, fluid soul and aching, theatrical balladry — and in substance, as it captures perfect images of American romance and cool like so many Polaroid snapshots. Few pop artists have ever been as effortlessly cool; still fewer have managed to create a piece of art that sounds like it could have been crafted thirty years before it was, or thirty years after. Pirates has been influential, but rarely imitated. Who could?

Her latest album, 2015's The Other Side of Desire, clearly has Pirates as an ancestor: the warm-blooded elasticity of her voice, her snappy fluency in the language of cool, and vivid lines like one rhyming "gold capped tooth" with "hot tin roof." With songs that borrow the language, the structure and the melancholy of a Cajun waltz, Fats Domino piano rhythms and swamp-pop melody, it's even more audibly rooted in her new (and old) home base — she's using the same storyteller's ear and the same keen eye for character, although both, now, she thinks, feel clearer.