Her high-profile musical collaborators have ranged from Willie Nelson, Keith Richards and Wynton Marsalis to Foo Fighters, Wayne Shorter and Tony Bennett.

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Her father is the late Indian music legend Ravi Shankar. She quietly visited him a number of times at his home in Encinitas, in California, which he shared with his wife, Sukanya, and Norah’s half-sister, acclaimed sitar player Anoushka Shankar. The two siblings, who met for the first time in 1997 as teenagers, memorably recorded together on Anoushka’s 2013 album, Traces of You.

Last week, Jones launched a tour celebrating the 20th anniversary of Come Away With Me, one of the bestselling albums of this century.

How, one wonders, has Jones remained so grounded and free of any of the affectations of stardom, let alone stayed out of the spotlight for so long when not performing?

“I think that’s partly due to my mom, my friends and the people around me,” replied the married mother of two. “Also, I was signed to a serious record label. I had an amazing publicist and marketing guy, but they were not courting that kind of [high-profile coverage].”

Her label, Blue Note, is one of the most famous jazz labels. Its roster is a who’s who of famous jazz artists and includes the singer Cassandra Wilson, who – with Billie Holiday and Sarah Vaughan – is one of Jones’ all-time favourites.

An alto saxophonist turned pianist and singer, Jones was signed by Blue Note when she was 21. Come Away With Me was released when she was 22, after two different recording sessions with two very different producers, Craig Street and Arif Mardin.

The recently released three-CD Come Away With Me 20th-anniversary box set features a remastered version of the final, Mardin-produced album. It also includes the earlier sessions she did with Street, plus a trove of alternate versions and outtakes.

The results offer fascinating permutations of the album. It also features 14 previously unheard recordings that illustrate Jones’ ability to put a fresh, distinctive stamp on such jazz standards as When Sunny Gets Blue and Spring Can Really Hang You Up the Most.

Of course, she had several distinct advantages as a young new artist making her first album. There were no commercial expectations to live up to, no pressure to make hit singles, no push to become a star.

“I didn’t feel I had to prove anything,” Jones agreed. “But I had to get it right. I felt a little pulled in different [musical] directions by people in my life – some friends, some [record company] executives, producers, whatever. I was just trying to stay steady and follow my own sense of self and keep it throughout.

“The last thing I wanted to do, after getting a record deal, was to make an album I didn’t want to make. I wanted it to be an album I liked, even if it wasn’t [commercially] successful.”

An understated gem that has aged very well, Come Away With Me is dominated by hushed ballads. They proved to be an ideal showcase for Jones’ supple piano playing and earthy-yet-elegant singing. Like very few artists in their early 20s, she caressed each note she sang and savoured the silences between them.

Drawing from jazz, blues, country and soul, the music on Come Away With Me was spare and unrushed. Jones’ music was greatly enhanced by the wonderfully sensitive accompaniment of musicians, including guitarist Kevin Breit, violinist Jenny Scheinman and drummer Brian Blade, who is also helming the drum chair on Jones’ current tour.

“I like stuff that’s understated, and I’ve always been drawn to ballads,” she said. “I can’t scat sing … and I can’t sing like Mariah Carey. But I don’t want to. It’s not what I enjoy listening to, so I went in the other direction.

“I don’t have a lot of chops on the piano. I don’t have any chops! I just play simple, and I like it that way. I don’t want to do something I don’t like. It’s just me singing the song. The ‘product’ is me. And when the product is you, you’ve got to be really careful. Because this is my life.”

Given the benefit of hindsight, what does Jones attribute her early success to?

“One thing I’ve noticed, looking back now at the box set, is that the album has a really hopeful sense of innocence to it,” she replied. “I never realised that at the time, because I was so young. I just thought at the time: ‘These are songs and maybe people will think they are melancholy, but I like them.’”

The speed with which her career took off can be illustrated by Jones’ early San Diego concert history.

In March 2002, she performed with two accompanists at the 600-capacity nightclub ‘Canes in Mission Beach. She was the opening act for John Mayer.

“I remember that very well!” Jones said. “I stood outside talking with John, looking at the ocean. That whole tour was so wild and fun. It was the first time I opened for someone like that and played venues that big.”

She returned in July 2002 to headline a sold-out show at the 1,450-capacity Humphreys Concerts by the Bay. Then came a sold-out July 2003 show at the 5,000-capacity SDSU Open Air Theatre. By October 2004, Jones was headlining at Chula Vista’s nearly 20,000-capacity Coors Ampitheatre.

“It was a whirlwind! And it was definitely turbo-speed,” she recalled. “But we adjusted as best we could, and I made changes here and there to sort of keep up with all of it. Sometimes it’s hard to hear the audience in big outdoor venues, so I had to get used to the sonics of being in huge venues and wearing ear monitors.”

Jones marvelled aloud at how profoundly her life changed 20 years ago. “I was so young and had no idea what was coming,” she said.

A jazz piano major, Jones dropped out of the University of North Texas in her sophomore year to move to New York. Her mother was not pleased.

“She was really unhappy. She really wanted me to not do that!” Jones recalled in a 2003 Union-Tribune interview.

“After I was in New York about eight months, I got very depressed. I was 20 and lonely, and I called my mom, crying, one night. I said: ‘I’m going to come back home to Texas. I’m sorry. Can I come back?’

“And even though she was mad I’d dropped out, she said: ‘Give it a year. Don’t give up so fast. Then come back, if you still want to.’ I thought that was pretty cool.”