Miles Kane, former member of The Rascals, and The Last Shadow Puppets, including Alex Turner of the Arctic Monkeys, did a great feature with Alison Mosshart of The Kills and The Dead Weather. It’s called Paris Summer and was originally done by Nancy Sinatra and Lee Hazlewood, given that I remember correctly.
Their version of Paris Summer is probably one of the best covers I’ve heard. And yes, given all the big names and references that shouldn’t be much of a surprise. Although there are a lot of crappy cover versions of great songs out there. Look at Leonard Cohen’s Hallelujah for instance. There was but one singer who got it right after Cohen, I would argue, and that was Jeff Buckley.
However, here is a video of Paris Summer by The Last Shadow Puppets and Alison Mosshart, shot for some French TV station (Concert Privé Canal+), take a look at listen to Alison’s fantastic voice: