OLD SAYBROOK >> In the liner notes of Rickie Lee Jones’ 2015 comeback album, “The Other Side of Desire,” the magnetic and unpredictable singer-songwriter, who will be doing her thing at The Kate on Thursday, Aug. 3, has a message for her fans.

“I am happy with the loss of prestige,” she writes.

Surprising words from the cultural phenomenon who was named by Time Magazine as the “Duchess of Coolsville” in 1979, took home a Grammy a year later, and twice graced the cover of Rolling Stone. Saturday Night Live gave her an unprecedented three songs for her appearance. A generation of women imitated her bohemian look.

The self-described product of a “lower-middle-class-hillbilly hipster family” was a certified rock superstar. “Chuck E.’s in Love,” her hit single, provided listeners a glimpse into the bohemian Los Angeles life she shared with then-boyfriend Tom Waits and their musician pal Chuck E. Weiss.

“Woody and Dutch on the Slow Train to Peking,” released in 1980, showcased a voice that, as music critic Hilton Als put it, “at times has the lonesome sound of a train whistle on a wind-swept prairie and at other times sounds like nothing so much as laughter winding down into a whisper or a sigh.”

And “Makin’ Whoopee,” her cover with Dr. John, featured on “Sleepless in Seattle,” gave her a second Grammy Award.

Then the wild ride ground to a halt.

“I knew my impact,” the 62-year-old said in a recent conversation. “With the tremendous success I had, it was a humbling and weird moment when I went ‘wow, it’s gone, it’s over, it’s not coming back.’ I think I spent 15 years trying to resuscitate it.”

For the artist ranked number 30 on the VH1’s 100 Greatest Women of Rock & Roll in 1999, “the creative juices were probably always flowing, they ebb and flow. But I had nothing to write about or didn’t have the impetus.” A move to New Orleans, after more than 40 years of living on and off in Los Angeles, she added, “was the catalyst for a better feeling about life, which in turn made room to write.”

The result, “The Other Side of Desire,” marked Jones’ first batch of newly-written songs in a decade and has the 62-year-old in the midst of a career renaissance.

The title of the album was inspired by her adopted city, where she lives on the other side of the street made famous in “A Streetcar Named Desire” by Tennessee Williams.

Typical of her unclassifiable style — her songs range across pop, rock, rhythm and blues, and jazz — the songs in “Desire,” while nominally hymning the Crescent City, don’t always have an obvious New Orleans sound.

Sure, there are the sousaphones and accordions in “The Circus of the Falling Star,” but not as Big Easy clichés; “they appear naturally, like regulars at the corner bar,” as Nashville songwriter Hall of Famer Gretchen Peters put it.

There’s also the raucous piano-based R&B of “J’ai Connais Pas,” a tale of a low-life set in a bar, sung over a walking Fats Domino piano riff with a French Creole twist. And the bayou-pop of the jaunty “Haunted.”

That said, there’s no doubt the scuffed-up honesty and humanity of post-Katrina New Orleans have permeated her songs.

There’s “Juliette,” a sweet paean to her dog; “Feet on the Ground,” an achingly beautiful minor-key meditation on damage and loss; and “Jimmy Choos,” a classic Jones narrative about an expensively dressed woman sitting on a rooftop and throwing bottles at the cops below.

“It’s not only Jones’ most absorbing work [in years],” British journalist Nigel Williamson writes, “but a record that crowns her career, not as an end but as a culmination.”

Among the reasons, according to Gretchen Peters: “Too many records get made, and too many songs written, because the artist or someone in her sphere felt an urgency to deliver a product, to fill a void,” she writes.

“Not ‘The Other Side of Desire,’” she writes. “It has an inevitability about it; it’s the work of an artist who spent time listening to her life, waiting for the songs to manifest themselves, and delivering them with honesty and compassion.”

Jones who, in her current incarnation, has ditched her signature red beret, had her own take. “Maybe what I found out is to look at my life as an arc and to cherish and celebrate every single passage, even the dark ones,” she said. “That’s what freed me up.”

So much so, she added, that “sometimes when I’m on stage, I feel like I’m floating up off the ground. That wasn’t always the case.”

Sounds exactly like an artist who’s not too concerned with prestige, lost or regained.

Rickie Lee Jones will appear at the Katharine Hepburn Cultural Arts Center, 300 Main St., Old Saybrook on Aug. 3 at 7:30 p.m. For tickets and information, visit thekate.org or call 877-503-1286.