For the last four years US pop superstar Kesha has had a huge but miserable media presence. Her bitterly fought court battle to be released from her contract with producer/alleged Svengali Dr Luke, which involved allegations of abuse and sexual assault, created reams of headlines and social media conjecture, but gave the lie to the notion that “all publicity is good publicity”. And there’s been almost no music in that interim. Now, however, minus the dollar sign that used to make up the “s” in her name, Kesha returns with all guns blazing, and the best of her third album takes the listener by surprise.

The mood of Rainbow is righteous fury, as might be expected. On the three opening tracks, this works brilliantly. The album’s opening lines, on the stadium-acoustic “Bastards”, are “Got too many people that I’d like to prove wrong/All these motherfuckers been too mean for too long”, and she doesn’t stint on the swearing from thereon. “Let ‘Em Talk” is an Avril Lavigne–style plastic punker and the cuss-crazed, Stax-on-speed “Woman” comes on like a rabid Amy Winehouse, courtesy of The Dap Kings’ horn section.

Kesha, however, also has a penchant for cheese and power ballads. Sometimes this works, as on the space-pop “Hymn”, but sometimes it’s less successful, as on the ultra-epic “Praying”. Dolly Parton pops in for the country waltz “Old Flames (Can’t Hold a Candle to You)” and Kesha let’s her hair down for a glam stomp on the “Monster Mash”-meets-Sweet “Boogie Feet”, but the best material arrives when she doesn’t curb her innate eccentricity.

There’s plenty of country flavour on Rainbow and it works well, from the kooky, albeit faintly stalker-ish “Hunt You Down” to the jolly, Eartha Kitt-goes-electro canter of “Boots”. The album’s closing tracks, the child-like, preposterous “Godzilla” and the excellent, five-minute cosmic strum of “Spaceship”, showcase a woman whose talent is only just starting to truly shine. In fact, turn this album into an EP of its best six or seven cuts and it would be 5/5 material, because Rainbow is a smart, sassy, well-calibrated return to the fray.

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Overleaf: Watch the video for "Woman" by Kesha

August is often a quiet month on the release front but theartsdesk on Vinyl came across a host of music deserving of attention. Now that even Sony, one of the biggest record companies in the world, are starting to press their own vinyl again, it’s safe to say records aren’t disappearing quite yet. On the contrary, the range of material is staggering in its breadth. So this month we review everything from spectral folk to boshing techno to the soundtrack of Guardians of The Galaxy 2.

Hoyt Axton’s songs were heard most widely when recorded by others. Steppenwolf recorded his “The Pusher” in 1967. It featured on their early 1968 debut album but was most pervasive in summer 1969 after it was included on the soundtrack of Easy Rider. Axton himself didn’t release a version until 1971, when “The Pusher” appeared on his Joy to the World album. The title track, another of his best-known compositions, had charted earlier that year for Three Dog Night. Back in early 1963 "Greenback Dollar", which Axton had co-written, was a US hit for The Kingston Trio.

He’s in his ninth decade, but with no signs of slowing down on stage or in studio, and the good news is that, while God's Problem Child may be no essential release, it remains hugely enjoyable – and that’s mainly down to the lucky seven new songs from Willie, cowboy koans co-written with producer Buddy Cannon.

Best Troubadour is Bonnie Prince Billy's musical tribute to his "forever hero", country singer Merle Haggard. Haggard was best known for his song "Okie from Muskogee", a wry homage to small-town Southern values. Students of country music, however, remember a different Merle – the armed robber turned musician and iconoclast. In his own bohemian way Bonnie Prince Billy, aka Will Oldham, is another sort of radical. And on Best Troubadour he interprets Haggard's artistic vision through 16 of his lesser-known songs.

The album opens with "The Fugitive", whose lyrics evoke the dirt and desperation of life on the run. Such a visceral feel was pure Haggard. The other songs in the collection continue to capture much of that sensibility. But tellingly, the effect is strongest when paying close attention to the words. For while the album encompasses various styles, from the country- shuffle of "Haggard (Like I've Never Been Before)" to the lounge jazz of "I Always Get Lucky with You", Oldham's quivering voice always manages to sound a little wistful and somewhat folky.

Perhaps that's inevitable. Still, by placing Haggard's material in a gumbo of folk, country, blues, and jazz, Oldham explores the relationship between Haggard and Americana. And that – a widescreen sense of the American heartlands – is the key to this album. These covers may not have the immediate appeal of the originals, but they feel deeper. Indeed, the more you listen, the more you find yourself lost in tales of trans-American heartache and adventure. The effect is both enriching and absorbing.

Of course, Best Troubadour is not an artistic statement like an album of originals, but nor is it intended to be. That's typical of Bonnie Prince Billy. Over 25 or more years he's notched up 30-odd albums containing all manner of gems and curios. Appropriately enough, such prolific and varied output is something else he shares with Merle.

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Overleaf: watch Bonnie Prince Billy and friends covering Merle Haggard's "Mama Tried" (not on the album)