Indie icon Cat Power — a.k.a. Chan Marshall — has been releasing fine albums of original material for more than 25 years, but imaginative covers have always been a big part of her sound: Her sparse debut LP, “Dear Sir,” which featured a song written by Tom Waits and one by This Kind of Punishment, set the mold for a carefully curated mixture of classic and contemporary tracks written by others.

“Covers” is actually Marshall’s third all-covers album. She released “The Covers Album” in and “Jukebox” in 2008, the latter arriving in the wake of “The Greatest,” the most commercially successful album of her career, an alternative/NPR-leaning hit that even reached No. 12 on the Billboard 200.

But ironically, Marshall reinvents and inhabits others’ songs so completely that they sound like originals, and “Covers” is no exception: The songs here veer from just-recognizable to barely recognizable at all, with the focus on her unmistakable voice, often gorgeously multi-tracked and highlighted by spare production.

That is certainly the case for the album’s first single, a take on Frank Ocean’s “Bad Religion,” which is fathoms away from his vaguely churchy 2012 original and sounds like, well, a great Cat Power song.

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Marshall brings an ironic twist on the second track, a cover of her own “Hate,” which is stark and solo on “The Greatest” but fleshed out with a full band here and retitled “Unhate.” Elsewhere, she returns the favor of Lana Del Rey’s cameo on her last album, 2018’s “Wanderer,” by covering “White Mustang”; there’s a woozy, ethereal take on the Pogues’ shanty-esque “A Pair of Brown Eyes” and an unhurried, completely unrecognizable version of Bob Seger’s “Against the Wind”; and a spare and appropriately menacing take on Iggy Pop’s 1979 song “Endless Sea” (which is almost comically sandwiched between the Seger song and her lovely, gentle rendition of Jackson Browne’s “These Days”).

The transformations aren’t limited to musical arrangements: Marshall delivers the Replacements’ “Here Comes a Regular” with a massively treated, relatively deadpan vocal, accompanied by piano and distant acoustic guitar, that brings a ghostly quality to Paul Westerberg’s wistful, unvarnished losers’ anthem.

Perhaps most unusual of all, a couple of tracks actually evoke other songs: Marshall’s torchy version of J.D. Miller’s country classic “It Wasn’t God Who Made Honky Tonk Angels” (first popularized by Kitty Wells but performed by basically every Nashville legend of the past 50 years) summons visions of Peggy Lee’s “Fever,” and her version of Nick Cave’s urgent, angst-ridden “I Had a Dream Joe” has an easy groove reminiscent of “I Put a Spell on You.”

The album closes with a hushed but comparatively straightforward version of Eddie Heywood’s “I’ll Be Seeing You,” which was immortalized in the 1940s by Billie Holiday — completing yet another stellar addition to the Cat Power canon, which is formidable no matter whose songs she’s singing.