Given that the Who's Live at Leeds is, by just about any estimation, one of the half dozen or so greatest in-concert albums in rock & roll history, it feels a bit cheeky suggesting that it might not even be the best one recorded in Leeds. But if you're into bootlegs, you've known for some time that the Rolling Stones had one of their finest nights in that same place where the Who all but bodily launched themselves into the hard rock canon. That performance is captured on a bootleg called Get Your Leeds Lungs Out, one of those field documents that can inspire all sorts of arguments amongst the cognoscenti.

You might, for instance, declare that recording from March 13th, 1971 the best thing the Stones ever did – suck it, Beggars Banquet – even though they couldn't be arsed to put out this singular document that melds grace, raw power, heartbreak, the soaring dual-guitar attacks of Messrs. Richards and Taylor, and the piss and panache of Mick Jagger in a manner quite beyond any official Stones product.

But if you've never wandered down the bootleg rabbit hole and were curious, the Stones' Leeds set has finally gained its sanctioned release on the Super Deluxe Edition of Sticky Fingers, tucked away on disc number three. This is the Stones saying farewell to England – thank the taxman for that – in a club setting, minus the outright terror of 1970's Get Yer Ya-Ya's Out, amidst a whole lot of bendy flow and slinking grooves and country nods bestride shuffling blues and torquing rhythms.

"Dead Flowers" is the kind of Stones song that no one calls an out-and-out classic, and yet it seems to rate as a favorite for many people, listeners who, doubtless, would want this killer live version. It kicks off everything here, Jagger giving voice to the pain of unrequited love in the clipped country accent of a Southern trucker, while Mick Taylor's guitar lines flow like liquid citrine underneath.

We've clearly joined the gig in medias res, but that simply serves to make everything feel more lived in, more like an experience and less like a straight-up show. "Stray Cat Blues" is full-on, glorious salacity – the line about a friend with an even wider, well, orifice, has a Chaucerian vulgarity to it that Jagger clearly relishes here – whereas "Love in Vain," has what might be the best solo Taylor ever uncorked, and comes off like something dredged up from the deepest loam of the Delta.

And then there is "Satisfaction," a number that, back on the 1969 tour, was like some asp taking musical form on the stage, with that attacking, slithering riff, and just having at you. Here, remarkably, it's a Slim Harpo groover, a rare blues shuffle in which every part is clearly delineated, from Charlie Watts' backbeat to the scud of Bill Wyman's bass, to the tandem guitars, to Jagger's horn-like vocal, which plays off the original 1965 single's horn-like riff. Come the closing romp through Chuck Berry's "Let it Rock," it is balls-on-the-table time, and a self-referential directive to basically rock harder than anyone else could. Call it a mighty, Leedsian reckoning. These are the Stones you need to hear.

On that score, here are five other stellar selections from that live bootleg basement, spanning the band's glory run, from its early days to the Exile era.