Which is worse: not to tell an important story, or to flub its telling? Journalist Gary Webb didn't commit either sin in 1996 when he published his "Dark Alliance" series in the San Jose Mercury News. The story alleged that, during the 1980s, the CIA knowingly countenanced Nicaraguan Contras who smuggled cocaine into the U.S. to bankroll their insurgency. That thriving drug trade gave birth to the era's crack epidemic.

"Dark Alliance" was compelling enough to ignite a firestorm of controversy — and scrutiny, which eventually ended Webb's journalistic career. (He committed suicide in 2004.) Fellow journalist Nick Schou chronicled Webb's travails in a 2006 book called Kill the Messenger, which argued that the powers that be buried his story precisely because the evidence supported it.

Based on both Schou's and Webb's work, this film from director Michael Cuesta portrays Webb (Jeremy Renner) as a heroic David brought down by the twin Goliaths of the CIA and the mainstream media. It's undeniably a story we need to hear. But, in the hands of Cuesta and screenwriter Peter Landesman, it's not a particularly compelling one.

The problem isn't the material but the timid, boilerplate approach. Webb's story offers golden opportunities for the sort of dramatic dissection of broken institutions that David Simon did so well in his HBO series "The Wire." Cuesta, who directed eight episodes of "Homeland," knows his way around tensely paced procedurals. He gives the early scenes of Kill the Messenger a tight, propulsive narrative, as Webb follows a tip from a drug dealer's girlfriend all the way to a Nicaraguan prison. There he meets a courtly former drug lord (Andy Garcia) with a damning tale.

Once Webb's story hits print, however, the movie stops being an absorbing case study of how a reporter pursues a great lead. What we're left with is a collection of persecuted-truth-teller clichés. Soon Webb's long-suffering editor (Mary Elizabeth Winstead) and publisher (Oliver Platt) turn from nuanced characters into turncoats who quickly betray him. When Webb visits a Washington player (Michael Sheen) in hopes of finding a source in the intelligence community, he's given the sinister, on-the-nose message that "Some stories are too true to tell."

Rather than exploring the voracious media culture that built Webb up and then tore him down, the film keeps the focus on the man himself. Nobody plays obsessive, unhinged characters better than Renner, as he showed in The Hurt Locker. In this role, his wild eyes match the frayed strap on his messenger bag, his sartorial sloppiness serving as a badge of journalistic virtue. (The film depicts the staff of the Los Angeles Times, which systematically picked apart Webb's story, as immaculately suited and tied.)

But the script is too busy building Webb up as a hero to give him a truly troubled or even interesting psyche. Sometimes real persecution breeds pathological paranoia, but Kill the Messenger waffles on the question of just how justified Webb's paranoia was. Instead of investigating his dark places, it treats us to scene after static scene of his home life with a loyal but worried wife (Rosemarie DeWitt) and a kid who just wants his dad back (Lucas Hedges). These actors deserve better than going through the motions of the tired "Daddy, why do you have to go save the world?" trope.

So does the audience. While the particulars of Webb's story are still disputed, a subsequent CIA report appears to support his central contentions. Hobbled by their limited approach, Cuesta and Landesman miss their chance to illuminate a world in which such revelations sank within a news cycle. There may be a story here about the last gasp of great shoe-leather journalism, but they're not telling it.