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Either the man’s slowing down or the subject requires a steady hand, but “Snowden” is Oliver Stone’s most subdued movie by a long shot. It creeps in on little cat feet, much like the mild-mannered figure at its center, the former CIA/NSA analyst Edward Snowden.

You probably already know how you feel about Snowden and about his revelations, in 2013, of the extent to which the US government was (and still may be) spying on you and me. If not, you should. At the very least, you need to come to terms with “Citizenfour,” the Oscar-winning 2014 documentary by Laura Poitras that puts us right in the Hong Kong hotel room with Snowden as he’s releasing to the public thousands of US and international intelligence files with the aid of journalists Glenn Greenwald and the Guardian’s Ewen MacAskill. That movie was made to serve as both evidence and insurance, and it is essential viewing.

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Stone’s version, by contrast, is less necessary but worthy of attention. Based on two books — the fictionalized, as-yet-unpublished “Time of the Octopus,” by Snowden’s Russian lawyer Anatoly Kucherena, and Luke Harding’s nonfiction “The Snowden Files” — it’s well and compellingly made, working hard to bring the blurry figure of Snowden into focus while dramatizing his transformation from patriotic civil servant to appalled citizen whistle-blower. The movie presents him as a hero, obviously, and it doesn’t have to strain to press its central thesis: that any government whose intelligence agencies secretly and routinely monitor the phone calls, e-mails, and Internet traffic of a majority of its citizens is guilty of Orwellian overreach.

“Snowden” wants to do more than numbers and outrage, though. The storyline spans the years from 2004 to 2013 and shows Snowden’s growing disenchantment with the intelligence community’s penchant for dirty tricks and collateral damage. One of our more underrated actors, Joseph Gordon-Levitt, has the title role; he can be an antic sprite in some movies but here he lowers his voice and slows his rhythms to become earnest, unsure, socially awkward. For most of the movie, Snowden knows far more than he can tell, and it paralyzes him.

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On one shoulder is the devil, Rhys Ifan as Snowden’s (fictional) CIA mentor, heavy-lidded with cynicism and realpolitik. On the other is the movie’s angel, his girlfriend Lindsay Mills (Shailene Woodley), a dancer-acrobat and all-around free spirit who often pushes back against her boyfriend’s professional wall of reserve. “Snowden” expends a good amount of energy on the couple’s arguments, separations, and reunions, and aside from formulaically “humanizing” the hero, these scenes don’t add a lot.

Much more interesting are the sequences in Snowden’s various places of business over the years: in Geneva with the CIA, where he gets a tutorial from a fellow agent (Timothy Olyphant) in how to use and destroy an informant; in Japan as a consultant with the NSA, where he learns from a fellow tech-wonk (Ben Schnetzer) how broad-ranging US surveillance really is; to an NSA bunker in Hawaii, where Snowden makes the decision to leak the documents and copies them to a thumb drive in one go, immediately leaving to meet with the reporters in Hong Kong.

The film’s created as a pointed entertainment, a case for the defense that also functions as an information-age horror movie, with the spooks in Tokyo peering through a random woman’s laptop camera to gawk as she disrobes. (Snowden immediately goes home and puts masking tape over Lindsay’s webcam.) There are excellent turns by Melissa Leo (as a motherly Poitras), Zachary Quinto (playing Greenwald as an arrogant jerk), Tom Wilkinson as MacAskill, and Lakeith Stanfield, his usual excellent, low-key self as a fellow surveillance geek who shares Snowden’s misgivings.

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Very late in the film, Snowden himself drops in, a ghost triumphantly appearing in his own biopic. Charged with two counts of violating the Espionage Act of 1917 — and hardly guaranteed a fair trial were he to return to the United States — he continues to live in Russia, where he has a three-year residency permit that allows for travel abroad.

In actuality and unlike in the film, it’s not at all clear that any of Snowden’s NSA peers approve of what he did. In addition, he appears to have begun collecting information as much as a year earlier than shown in “Snowden.” There are other gray areas to which the director applies white paint, and while that may not change the awful truth of what our intelligence industries have done and want to do it makes the movie a secondary object to this story. As always, it’s a good idea to do your homework before or after seeing an Oliver Stone movie. You may come out convinced of his point of view and still feel hustled by how he got you there.

★ ★ ★
SNOWDEN

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Directed by Oliver Stone. Written by Stone and Kieran Fitzgerald. Starring Joseph Gordon-Levitt, Shailene Woodley, Melissa Leo, Zachary Quinto, Rhys Ifans. At Boston Common, Coolidge Corner, Fenway, Kendall Square, suburbs. 138 minutes. R (language, some sexuality/nudity)


Ty Burr can be reached at ty.burr@globe.com. Follow him on Twitter @tyburr.