Back in 1995, when she was opening shows for Liz Phair — then indie rock’s exemplary “It Girl” — Chan Marshall was a transcendental mope. Her singing was so whispery, her stagecraft so inept, that the introspection common to someone working in the “sensitive songwriter” mode became a painful introversion. To watch Ms. Marshall, a waif-like being who always strummed under the name Cat Power, was akin to discovering a wild child, someone unencumbered by society’s conventions, yet awkwardly ill at ease when fetched into the spotlight.

If that made for a raw psychic exposure that seemed worlds away from the clever wordplay and strident poise essayed by Ms. Phair, whom Cat Power would eventually succeed as Matador Records’s reigning diva, it also made Ms. Marshall’s concerts impossible anti-spectacles. When I lived in Atlanta, the singer’s home base for much of the 1990s, everyone was in love with her. She had a mini-cult of admirers almost from the start. The collective adoration, which would grow by international degrees during the next decade, was whetted by the incongruous gap between the singer’s evident allure and her confounding diffidence. As Patterson Hood, singer for the Athens-based rock band the Drive-By Truckers, once declared in a song called “Cat Power”: “You little misguided artist you / You know deep down I’ll root for you.” No one could have said it better.

Ms. Marshall was far from the most talented vocalist in town. And for all her enigmatic airs, which could mostly be attributed to shyness, she was scarcely the most eccentric figure on the local underground scene (the late Benjamin, drag queen/speed freak frontman for the bands Opal Foxx Quartet and Smoke, took that prize). But performance-wise, she was in a class all her own: There was no one so exasperating. No matter how smoky and mysterious Ms. Marshall’s twilight grunge-folk sounded on record, the concerts sucked.

But the albums, beginning with her third release, 1996’s “What Would the Community Think?,” got better and better. Though she often toured alone, or with a pickup band of musician friends from Atlanta or New York, Ms. Marshall was choosier in the studio. On 1998’s “Moon Pix,” she initiated a rewarding partnership with the guitarist Mick Turner and drummer Jim White of New Zealand’s Dirty Three, and finally became secure in her 3 a.m.-of-the-soul evocations, spectral and quavering like a country porchlight glimpsed through Spanish moss and pre-dawn mist. Her voice hovered in the same vulnerable alto range as the later-emergent Beth Orton, and the folk-based songs, with their ragged edges, were frazzled like Neil Young’s. If Ms. Marshall offered a template for a generation of composerly and photogenic Starbucks-friendly singers — from Norah Jones to Feist — whose ambivalence went down smooth as a latte, she proved thornier.

She still does. Ms. Marshall’s new record, “Jukebox,” out today, capitalizes on the breakthrough of her radiant “The Greatest,” the 2006 album that saw the singer step up to the challenge of working with a “real” band — an all-star assortment of such old-school Memphis studio masters as the guitarist Mabon “Teeny” Hodges, who co-wrote many of Al Green’s hits, and drummer Steve Potts, from Booker T. & the M.G.s. The project reflected Ms. Marshall’s personal obsession with the iconic aura of Memphis as a key site in the civil rights-era South and gave her the chance to mesh her formerly bare-boned songs with those lush, simmering Stax/Volt grooves.

It also worked transformative wonders in concert, as a performer who formerly verged on the autistic flowered into something like professional maturity. Last summer, as she headlined at Chicago’s Pitchfork Media Music Festival, Ms. Marshall still had her mojo intact. Her group, an offshoot called the Dirty Delta Blues, was killer, featuring the tastefully nuanced Mr. White on drums and Judah Bauer, the eruptive guitarist from Jon Spencer’s Blues Explosion. The outfit’s rewired versions of Dusty Springfield and Otis Redding felt at once classic and contemporary, with Ms. Marshall’s self-conscious mannerisms undoing memories of the pop standards even as she remade them.

“Jukebox,” a collection of covers, works entirely in that vein. Amid songs by Joni Mitchell, Hank Williams, and Janis Joplin, there’s stuff here that just sounds odd (“New York, New York”), because it thoroughly discards the original melody and becomes a caprice. There’s also stuff that sounds perfect, like the version of Bob Dylan’s hymn “I Believe in You,” with Ms. Marshall emoting over rough drums and raw guitar that could be an outtake from “Exile on Main St.” The Rolling Stones are frequently evoked (and not just on the cover image, which finds the singer copping a Mick Jagger strut). George Jackson’s “Aretha, Sing One for Me” is a joyous evocation of the late-1960s gospel-grunge that the Stones claimed during their own infatuation with Southern roots music. A retake of James Brown’s “Lost Someone” strips away even that veneer, as Ms. Marshall delivers the lyrics with a spartan ardor, accompanied only by some echoing guitar and brushed drums.

As much as “Jukebox” is about hero worship, Ms. Marshall achieves her own pinnacle when she pens the lyrics — about hero worship — in “Song to Bobby.” It’s a catalog of moments in which her life might have intersected with that of Mr. Dylan, whose concert T-shirt she infamously modeled for Richard Avedon in the New Yorker, her jeans zipper loosened enough that we couldn’t print the image in this newspaper. Oh, the things she wanted to tell Bobby if they met. The music, with subtle piano notes and a contemplative medium tempo, is gently imagined as a backing track from some circa-1965 Dylan studio session. Ms. Marshall sings at her wispiest, here and there inflecting with a bit of Bob in her larynx — as she does on a resplendent version of “Stuck Inside of Mobile (with the Memphis Blues Again),” from the recent “I’m Not There” soundtrack. It’s moving because it’s so personal, and because her voice gives way when she pushes for meaning. There are no mannerisms, and no professional poise, either.

In her desire to embrace her own spiritual heroes, Ms. Marshall may not become their equal, but perversely enough, she’s never sounded more original. On “Jukebox” she’s transcendent, but she’s no longer moping.