You've seen the photo: the King of Rock 'n' Roll and the Leader of the Free World, shaking hands in the Oval Office with cautious smiles and dazed looks in their eyes. Elvis & Nixon is an account—from director Liza Johnson and co-writer Cary Elwes—of that bizarre meeting in 1970. It's a piece of blissfully speculative fiction that takes its small but amusing concept and runs with it.

It's hard to go wrong when you cast Michael Shannon as Elvis Presley and Kevin Spacey as Richard M. Nixon: Shannon's Elvis is a soft-spoken, impressionable, lonely man who's adrift in the cultural sea change of the late '60s. He wants to save an increasingly anti-war, pro-drug America from itself—but more importantly, he has the cockamamie idea that he'd like to be an undercover federal agent. (As if no one would recognize one of the handsomest, most flamboyant men in history.) Spacey's Nixon, meanwhile, is a prickly, self-centered ass (of course), but one who can't suppress a politician's deep-rooted need for approval. He's harried by his job and a little confused by how much America's youth detest him. Nixon and Presley had a surprising amount in common: Here were two of the most paranoid people on the planet, and two of the most arrogant—and seeing Shannon and Spacey dig into them is as pleasurable as you'd imagine.

The movie only goes awry with its audience-proxy character: Elvis' handler and friend Jerry Schilling, played by the supremely uninteresting Alex Pettyfer. Colin Hanks does far better as a pre-Watergate Bud Krogh—an Elvis fan who sees a way to rehabilitate Nixon's unpopular image. And when it happens, the ridiculous Nixon/Presley encounter itself is given just the right touch. Elvis & Nixon's contained scope and underplayed humor make for a deft, lighthearted comedy about two pretty tragic dudes. recommended