For many who’ve seen Cat Power gigs over the years, calmness is not a word that immediately springs to mind when trying to describe Chan Marshall. Neither has she been, for large tracts of her confounding and exceptional career, much of a populist, exactly. Her distrait otherness might have been part of the appeal to some of us, but it would hardly work as a mainstream draw.

Since last year’s “The Greatest”, however, Marshall seems to have become more than a hip name to drop amongst indie fans and fashion industry types. If she could just hold things together for long enough, maybe, maybe, she could narrowly sneak into the record collections of a few Norah Jones fans, too.

“Jukebox”, her new thing, definitely builds on that. It’s predominantly a covers record, but the contrast between it and 2000’s “Covers Record” is vast. Where that album was frail, almost disconcertingly so, and skeletal, “Jukebox” is a little more fleshed out, and blessed (or cursed, depending on how much of a casualty you want Marshall to sound) with an elegance and calmness. She used to sound ghostly, hushed, as if she were barely there. Now, Marshall doesn’t belt them out, exactly. But the engaging slightness of her vocal performances seems the product of discretion rather than debilitating confidence issues.

What I’m trying to say, I suppose, in a typically ambulatory way, is that “Jukebox” is a very tasteful record, and consequently may alienate some of her older fans. Her treatments of songs here – by Hank Williams, Bob Dylan, Janis Joplin, Joni Mitchell – is far from orthodox. But while she takes a standard like “New York New York” and shimmies her way around the familiar melody, there are no striking deconstructions like that of “Satisfaction” on “The Covers Record”. These are often radical and soulful rethinks, but they don’t like stream-of-consciousness gushes from Marshall’s psyche. She inhabits these songs, sure, but this time she stops short of stealing their bones.

Part of this is due, I guess, to the measured classicism of her current band, the Dirty Delta Blues. Jim White’s been on call with Marshall for years now, of course (interesting to contrast “Jukebox”, incidentally, with another of White’s recent gigs, PJ Harvey’s “White Chalk”; there are vague affinities between Marshall’s rethink of her own “Metal Heart” here and some of Harvey’s fine work. In general, though, the two singers seem to be currently moving in opposite directions). But Judah Bauer from the Blues Explosion is a big, if still fairly subtle, presence: it’s his spare, clipped Keith riffs that drive the take on Dylan’s “I Believe In You” (less deferential than their “Stuck Inside Of Mobile” on the “I’m Not There” soundtrack, I’d say).

More deferential, oddly, is “Song To Bobby”, which follows straight after. This is Marshall’s explicit and very touching homage to Dylan. As Woody Guthrie was to Dylan, so Dylan becomes to Marshall, when she goes to meet him backstage at a gig in Paris. For most of “Jukebox”, Marshall’s voice is strikingly unfussy – one of the album’s pleasures is how she consistently refuses to believe that oversinging is the only way to impose emotion on someone else’s song, so that she can handle Janis Joplin and Billie Holiday showstoppers with striking understatement.

But on “Song To Bobby”, something strange happens. It’s rather touching, actually; her voice takes on the flip, accelerated phrasing of early Dylan. “Jukebox” is a gorgeous record, if lacking the diffident punch of some of its predecessors, notably “You Are Free”. But when she affects Dylan on her own song, Marshall cleverly points up the cleverness of the whole endeavour.

Here, more than anywhere else, you think most about the art of the cover, the purposeful and inadvertent acts of impersonation that go with it. By including “Song To Bobby”, Cat Power hasn’t just made an album of covers, she’s made an album about covering songs, too. Interesting.