“Elvis & Nixon” is only yea-big, and it’s not intended to carry the usual biopic baggage, but its particular charms are disarming nonetheless.

It’s fun to watch Michael Shannon and Kevin Spacey do their thing without settling for impressions or impersonations. These fine actors evoke and explore, rather than replicate. In a wryly comic but unshticky vein, they imagine for us what the two most disparate Americans in American history were like behind closed doors, and why they may have found some common ground, if only fleetingly.

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The photo and the meeting inspiring director Liza Johnson’s pocket-size film have become the stuff of unlikely historical legend. On Dec. 21, 1970, Elvis Presley, the king of more than mere jumpsuits, was granted a sit-down with President Richard M. Nixon in the Oval Office. Presley’s semi-legible letters to the president, hand-delivered to the White House security guards, stated his reasons for the meeting: to offer his services to his country as an undercover federal agent “at large,” perhaps to intercept drug deals, or bust up a Black Panthers meeting.

“Elvis & Nixon” treats the encounter neither dead-serious nor as an 87-minute punch line. Alex Pettyfer and Johnny Knoxville play Presley’s confidants Jerry Schilling (who wrote the book “Me and a Guy Named Elvis”) and so-called Memphis Mafia crony Sonny West, who accompanied the singer to the White House. Colin Hanks skitters around the edges of the meeting as Nixon aide Egil “Bud” Krogh, who wrote his own account of the handshake, “The Day Elvis Met Nixon.”

Shannon’s Presley gets just enough of the swagger and strut and soft-spoken quality down pat to let you forget the ways he doesn’t resemble Elvis. Spacey’s Nixon voice is exact but lightly worn, which allows us to absorb how much of the classically uncomfortable Nixon body language the actor nails.

The movie is less ambitious or probing than it might’ve been. But it’s a good one, and the actors go to town without turning “Elvis & Nixon” into a chance meeting between an Elvis impersonator and Rich Little.