The pop-music world, in many ways, has only gotten angstier (it would be hard to imagine a mood-poet chanteuse like Billie Eilish commanding arenas 20 years ago). But even back in the ’90s, Sheryl Crow was the kind of straight-up, middle-of-the-strike-zone, tasty-licks virtuoso of rock ‘n’ roll good times who seemed to have been put on earth to make people happy.

She was at the forefront of a revolutionary wave of women in pop — the Lilith Fair generation, from Alanis Morrisette to Sarah McLachlan to Shawn Colin to Paula Cole — but she was also, you could argue, one of the last great rockers to work in the heart-on-the-sleeve, guitar-riffs-on-air tradition of Bruce Springsteen and Tom Petty. My favorite line of hers has always been the one that comes after “All I wanna do is have some fun…” — namely, “until the sun comes up over Santa Monica Boulevard.” With her starburst smile and electrifying vocal bravado (which was always rock with a drop of country, befitting someone who came from “the bootheel of Missouri”), Sheryl Crow was someone you could imagine standing against the rising L.A. dawn after a night of partying.

In her songs, Crow has always been a vibrant crafter of her own mythology, telling it like it is. So when I went in tonight to watch “Sheryl,” the documentary portrait of her that was one of the opening-night films of this year’s SXSW Film Festival, I was ready to experience the wholesome, uplifting backstory of a supremely centered artist who has never had the inclination to bullshit you. All of that is true about her. But it doesn’t mean there isn’t some major dark drama to the Sheryl Crow story.

Her first big break was landing a spot as a backup singer on Michael Jackson’s 1987 tour, and she was already so self-possessed that when she was moved, in her big hair and spandex dress, to center stage to sing the nightly duet with Michael on “I Just Can’t Stop Loving You,” the tabloid press went wild, convinced that she and Jackson were having an affair. (You might explain that by saying: That’s how great a singer Sheryl Crow is.) The media attention thrust Crow into the spotlight, but things went awry when Jackson’s manager, Frank DiLeo, a fearsome figure with underworld connections (so authentic was his gangster aura that he was later cast in “GoodFellas”), told Crow that he wanted to manage her as well — and tried to force the issue, all as a form of sexual harassment. For Crow, this was a nightmare, one that sunk her into the first of several stressed-out depressions.

With the help of her friend and future manager, Scooter Weintraub, Crow was able to shake herself free of DiLeo’s grip. But the darkness wasn’t going to let her go. Her first album, “Tuesday Night Music Club” (1993), was named after the consortium of L.A. hipster musicians whose weekly music-and-drinking-and-philosophizing sessions became the roots-rock Petri dish out of which Crow formed her band. The album, led by “All I Wanna Do,” took off overnight, and we see her first talk-show appearance — on “Late Night with David Letterman.” Crow, in the documentary, deconstructs that interview for us, which is fascinating because we’re able to take in both the star-is-born who’s sitting on Dave’s couch, trying to laugh off his aggro irony, and the intensely nervous individual who that star still was. When he throws out a dumb question, asking if the song “Leaving Las Vegas” was “autobiographical,” she doesn’t know what to say and grins “yes.” She then spends the next minute backing off from that answer (and at one point hinting that she’d like to leave Dave’s couch).

But the damage had been done. The title “Leaving Las Vegas” had been borrowed by its composer, David Baerwald, from the novel by John O’Brien (which became the basis for the 1995 Nicolas Cage film), and O’Brien had been told that he’d get to share rights to the song. He thought that Crow, on “Letterman,” was claiming the song for herself, and shortly after that he committed suicide. There were some who blamed Crow for this tragedy — as if her late-night banter, at a moment when she was scrambling to gain composure, were anything more than forced frivolity. The incident, she says, tore her apart.

“Sheryl” tells these anecdotes, and others, in a swift and captivating fashion, with the director, Amy Scott, in engaging command. Scott has made only previous film, “Hal,” her portrait of the New Hollywood director Hal Ashby, and that was an interesting but minor effort, flawed by its rather glancing treatment of Ashby’s demons. “Sheryl” is both a fuller and more confident piece of work. It was made in full cooperation with Sheryl Crow, who’s a great storyteller because she’s an ace psychologist of her own mishaps. She cops to how obsessive she was, and is, about work — the way that recording and touring became an addiction, but also about the question she feels hangs over her entire career: “What are you going to sacrifice, as a woman, to be allowed to do this?”

Crow’s first pegs into show business are rather amusing: a McDonald’s commercial that earned her the equivalent of two years’ salary back when she was a fourth-grade teacher (she immediately quit and moved to L.A.), and a singing appearance on the final episode of the legendary jaw-dropping musical TV detective series “Cop Rock.” But she always knew what she wanted to do. She was a home-recording artist who laid out her musical vision on four-track demos, and after the first album’s triumph at the Grammys catapulted her, she followed it up by becoming a producer on her second album, demonstrating that the original was no fluke. It was her sound: sexy and muscular, as sweet as a sundae but with a free-flowing Cali-rock vibe.

In Paris, Mick Jagger called her at 4:00 a.m. to ask if she’d perform with the Stones, and when we see her on stage, singing a duet with Mick on “Live With Me,” her bravado is overpowering. She doesn’t defer to Jagger — she just about leads him. Keith Richards, interviewed in the film, testifies, with a twinkle of admiration, to that quality in Crow. The doc has some brashly captivating supporting players, like the sound engineer Trina Shoemaker, who’s like a Kate McKinnon character (she talks about recording equipment as if it’s alive). And there are amazing clips, like Crow‘s onstage duet with Prince singing a soul version of “Everyday Is a Winding Road” or her electrifying performance of “Home” at Lilith Fair.

Crow’s story appears, in many ways, to be a happy one. She has great parents, a dog who accompanied her on 13 tours, and two adopted sons she speaks of with a devotion so eloquent it’s heartbreaking. Yet she’s honest about the way that her success, at certain points, nearly broke her. Some might regard this sort of thing as the most cooked-up dimension of a music doc made in cooperation with its subject — the part where she complains about the perils of celebrity.

Except that “Sheryl” brings us close to the unreality of it all. Crow says that’s what the song “Strong Enough” is about: the challenge, for her, of finding a man who could stand up to the impossibility of her fame. She thought she’d found that in Lance Armstrong, but in the film’s brief sketch of their relationship, she says that the fallout from his doping scandal is what broke them apart. At the same time, she’s had three engagements, and she acknowledges that running — away from a partner, or to another city — is a pattern for her. It’s one that we’ve seen in other artists of her stature, but Crow presents her own triumphantly down-to-earth version of it. She’s funny, in a deprecating way, about what it means to be a “legacy” artist — someone from another era, but one lucky enough to stick around. Her life, to judge from “Sheryl,” will always be fraught, as surely as what happens on the rock ‘n’ roll stage will always be her escape to a perfect world.