When the Stones began recording Sticky Fingers on their ’69 American tour, the deadly chaos at Altamont hadn’t yet taken place. But when the completed album finally appeared in ’71, it showed a wiser band for a new decade—yet it’s still full of exhilarating strut and rumble. They pushed racial boundaries on “Brown Sugar,” while “Sister Morphine” is a fever dream about addiction. “Sway”'s lyrics are buried in one of the band's most battering performances, but they reach for redemption on the stunningly beautiful closer, “Moonlight Mile."