If any of the horrific scenarios sketched by Countdown to Zero  comes true, this nuclear-threat documentary will look timid in retrospect. But in a world where such weapons haven't been used since the year they were first available, the movie appears at times to be overselling its prophecy of probable obliteration.

Riffing on a John F. Kennedy Jr. speech about the dangers of nuclear explosives, director Lucy Walker explores the late president's three possible paths to radioactive cataclysm: "accident, miscalculation, madness."

The first two words are nearly synonymous, and cover a range of historical incidents in which someone — most often a Russian or an American — almost authorized a nuclear attack. The third is taken to refer to terrorism, and prompts the film's most alarming section: a discussion of the ease of building bombs and smuggling highly enriched uranium. (One way to fool the sensors: Hide the bootleg uranium in a shipment of kitty litter.)

The movie opens with a pocket history of the A-bomb, featuring cameos by J. Robert Oppenheimer and Enrico Fermi. Then it spins though Mumbai, Madrid, Oklahoma City and other metropolises hit by devastating (but non-nuclear) attacks. New York is featured, as it will be again and again as the movie progresses — although it's unclear if Walker considers the city the most likely target or simply the most recognizable one.

Such WMD veterans as Jimmy Carter, Tony Blair, Robert McNamara, Mikhail Gorbachev and Valerie Plame Wilson recount unnerving anecdotes: Aum Shinrikyo, the murderous Japanese cult, tried to buy a nuke. In 1961, mutinous French officers in Algeria actually nabbed one. In 1995, only Boris Yeltsin's common sense prevented a nuclear exchange after an American test missile was mistaken for an assault. And the U.S. has lost several nukes, most of which are still submerged in various large bodies of water.

The documentary shows how easy it is to obtain fissionable material from the weaker remnants of the former Soviet Union. It also introduces Pakistan's A.Q. Khan, "father of the Islamic bomb" and a conduit of technological knowledge to Iran and Libya. (None of this will be news, of course, to people who follow current events.)

Walker's style tends toward the flashy, with quick-cut missile-launch montages and computer-animated diagrams of rotating bombs and launchers, set to insistent rock tunes by Radiohead, Pearl Jam and the Cure. Clips from the apocalyptic black comedies Dr. Strangelove and From Dusk to Dawn also undermine the movie's grave demeanor.

The nine countries known to have nuclear bombs currently possess about 23,000 of the things. Oddly, Countdown to Zero ends by suggesting that viewers get those nukes abolished by texting their disapproval to a phone number listed in the credits — as if the governments of China or North Korea (or the United States, for that matter) are just waiting for a gentle rebuke from civic-minded documentary viewers.

In fact, the movie's account of the nuclear era reminds us that, since Nagasaki, no government has dropped the big one. The most menacing scenes involve the possibility of a nuke's being detonated by cultists — not known for being influenced by outsiders' text messages — or random error. "Low-probability events happen all the time," says one scientist, a line that's scarier than all of Countdown to Zero's blast maps and vistas of urban destruction.