This 1970 documentary, directed by Denis Sanders, captures singer Elvis Presley in his late-baroque, macramé hip-belt stage as he first rehearses and then performs live in Las Vegas, a limited residency in the desert town that became the stuff of legend. The material, released before in slightly different versions, has been dusted off and digitally gussied up for a one-night-only engagement in cinemas nationwide.

This is the 2001 cut, which has more performance footage and fewer cutaways to fans rhapsodising about the King and shots of him just hanging out with his entourage post-gig. No doubt that will make it a more attractive package for feisty public viewings, a more “event cinema” edition. But that means sacrificing some of endearing original documentary elements that make this such a time capsule, especially the full range of super-groovy, late 1960s/early 70s textiles in all their op-art, polyester glory. Some digital designer should work out a way to forensically recreate some of the shirt prints on display here, especially Elvis’s psychedelic purple, orange and chocolate-brown crushed velvet number that he wears for a rehearsal of That’s All Right Mama, accessorised with a white towel draped round his neck to soak up the sweat.

It’s a debate as old as time as to what’s the best Elvis period – young, hip swivelling idol, or chunky, past-his-prime showman – and this film captures him definitely towards the latter end of the spectrum, when he was still full of confidence but hungry to please. Musically, the most enchanting scenes are those that capture him joshing and jamming with the band, whether it’s with a mash-up of Little Sister morphing into a cover of Let it Be, or working with the backing singers on the choir-style crescendo for Bridge Over Troubled Waters. It’s these off-hand spontaneous moments that really capture just how drenched he was in talent and dedicated to his craft.

• Elvis: That’s the Way It Is is released in UK cinemas for one night on 13 August.