Prolific director Michael Winterbottom usually flies under the radar, as it were, making small but challenging pictures that have sometimes turned out terribly (the dreadful “Nine Songs”) but more often have been extraordinarily fine (to look only at his most recent films, the remarkable—though in very different ways—“In This World” and “Tristram Shandy: A Cock & Bull Story”). “A Mighty Heart” represents his first “mainstream” picture—one bankrolled by a major studio with a big star in the lead.

That doesn’t mean Winterbottom’s sold out, though. He tells the story of the frantic month-long search for Daniel Pearl, the Wall Street Journal reporter who was kidnapped and killed in Pakistan in 2002, in the same methodical but intense style he’s previously brought to similarly fact-based material in independent films (“In This World,” for example). It’s not unlike the skill at docudrama that Paul Greengrass applied to “United 93,” and if the result isn’t in the same league, given the pitfalls of the project the director’s achievement is considerable.

In the hands of Winterbottom and John Orloff (who based his script on the book by Pearl’s widow Mariane), “A Mighty Heart” is basically a police procedural set within the context of international politics in the age of post-9/11 terrorism. Pearl (nicely played by Dan Futterman) and Mariane (Angelina Jolie) are in Karachi, where he’s arranged a meeting with a sheik with terrorist connections. When he disappears during the encounter, his wife contacts the home office of the Journal and the American embassy, and soon U.S. security official Randall Bennett (Will Patton, convincingly understated) the Captain (the excellent Irffhan Khan), head of the new Pakistani counter-terrorism unit, and cop Dost Aliani (Adnan Siddiqui) are leading a concerted effort to identify his abductors and find Pearl, an effort that grows increasingly frantic as the kidnappers publicize their action and broadcast images of their victim with threats to kill him. (The chief suspect comes to be a shadowy figure named Omar Saeed Sheikh.) Mariane must try to maintain a semblance of control in the face of mass media coverage, supported by Journal honcho John Bussey (Denis O’Hare), who comes to Karachi, and the Pearls’ close friend Asra (Archie Panjabi).

Orloff and Winterbottom handle the complexities of the investigation with exceptional clarity and precision, offering the necessary explanatory details but not letting the narrative get bogged down in them. The director deserves special praise in this regard: he keeps the story moving in jagged, energized spurts without allowing it to descend into murkiness or obfuscation. (He’s helped enormously by the gritty camerawork of Marcel Zyskind, who, working on digital video in difficult locations, gets almost painfully atmospheric results, and Peter Chistelis’ sharp, edgy editing.) And while the narrative doesn’t flinch from depicting the corner-cutting methods (including torture) employed in tracking down the perpetrators, it neither glorifies them in testosterone-raising “24” fashion nor frames them as a PC-style critique. And despite the fact that we know the tragic conclusion to which the story is headed, the picture generates considerable tension while refusing to sensationalize the horrifying outcome by making it overly explicit.

But as fine as his work—which includes securing strong turns from his supporting cast across the board—is, Winterbottom doesn’t manage entirely to transcend the problems inherent in moving from his usual seat-of-the-pants methods to a bigger, more high-profile production. The difficulty derives mostly from the presence of Jolie. The actress has to be praised (along with significant other Brad Pitt) for championing this project, and she’s actually very good as Mariane, fashioning a woman who’s strong and sharp-tongued as well as deeply concerned and fearful (no milquetoast wife at all)—a performance that proves she’s a real actress, not just a star.

But there are moments when Jolie, as famous as she is, can’t help but be somewhat distracting, despite the attempt of the makeup artists to make her a bit less conspicuous. And one wonders whether, if a lesser name had been cast in the part, Winterbottom would have resorted to so many flashbacks showing Daniel and Mariane in happier days—the kind of thing one would expect in the work of lesser directors as a means of satisfying the audience’s need for some respite from a dark, depressing narrative—or would have included the scene of the widow’s emotional breakdown after learning of her husband’s death in quite so extended a form. (To be sure, he stages the latter discreetly, deliberately understating the histrionics, but they’re still there, and it’s one of the rare times when the film seems overly theatrical.)

Despite the flaws, however, “A Mighty Heart” proves a mostly effective recreation of a terrible event in the post-9/11 world. Like “United 93,” it can be described as a film that people ought to see from a sense of obligation, but like Greengrass’ picture, it makes its point without falling into the Stanley Kramer trap of becoming obvious and smugly didactic about it.

And if it might lead viewers to do some investigating themselves—of the earlier films of Michael Winterbottom, for example—it will have served a useful cinematic purpose, too.