YOU’D BE CORRECT to expect something bombastic out of Oliver Stone’s Snowden. It’s right in the JFK director’s wheelhouse, dealing in themes of power, corruption, and deeply conflicted American patriotism, with a vast government conspiracy perched on top of the sundae like a poisoned cherry. But surprisingly, Stone takes a calm, almost measured approach in telling the story of Edward Snowden, the defense contractor who blew the whistle on the American government’s theft of its citizens’ private information.

This is likely because the real Edward Snowden never cut a particularly dramatic figure. Joseph Gordon-Levitt plays the soft-spoken, squirrelly computer whiz with the right amount of awkwardness, resisting the bait of Stone’s tendency to turn heroes into martyrs. The supporting cast is similarly even-headed, including Shailene Woodley in a thankless role as Snowden’s long-suffering girlfriend and quick appearances from Nicolas Cage, Melissa Leo, Tom Wilkinson, Rhys Ifans, Timothy Olyphant, and Atlanta standout Keith Stanfield.

If you only know about Snowden from glancing at the headlines, or if you thought Citizenfour sounded like something you ought to see but never quite got around to, Snowden offers an easy-to-follow primer. Stone gets many things right, beginning the film with Snowden’s clandestine meeting with reporters in a Hong Kong hotel room and filling in the gaps from there. He has a few noticeable stumbles along the way, particularly when the film deals with Snowden’s epilepsy and his boring relationship woes. And things become unglued at the very end, when Gordon-Levitt disappears and the real Edward Snowden takes over the role.

Apart from that turn, Stone’s audacity is in little evidence, which is either a merit or demerit, depending where you come down on his work. A handful of shots through refracted lenses display Snowden’s growing paranoia, but otherwise this is largely a straightforward, sober handling of the material. Snowden himself might not be that interesting, but he did something extraordinary.