There’s a good deal to be said for understatement in a movie, especially one that deals with matters that can easily become overheated. But ironically “The Lucky Ones” takes reticence to excess. It concerns injured soldiers coming back from Iraq, a subject that was treated rather hyperbolically by Kimberly Peirce in the recent “Stop-Loss.” Here, though, the style adopted by Neil Burger {“The Illusionist”) is so laid-back and plain that the film leaves almost no impression at all.

The picture follows three GIs returning after the tours. Cheaver (Tim Robbins) is a reservist, injured in an accident (involving a portable toilet, ha-ha), who’s glad to be free of the service and, after two years’ absence, anxious to reunite with his wife and son in suburban St. Louis. Colce (Rachel McAdams) is southern girl, recovering from a leg wound, who plans to spend her thirty-day leave in Las Vegas visiting the parents of her boyfriend who was killed in Iraq, and returning his valuable guitar to them. And TK (Michael Pena) is an ambitious, rigid young man planning to get some unorthodox treatment in the same city for a shrapnel injury that’s left him unable to perform sexually before continuing on to California, where his fiancee lives. Unfortunately, when they arrive in New York from Germany, they find air traffic snarled as the result of a blackout and decide to pool their resources, rent a car and drive together to Missouri, where they’ll go their separate ways.

Of course, things don’t turn out quite as planned. Cheaver’s homecoming goes badly, and he suddenly finds himself homeless, unlikely to get his old job back, and in need of a wad of cash. He decides to continue westward with the other two, prolonging the picaresque road trip that’s already featured that old standby, a barroom brawl instigated in this case when some snotty college girls ridicule Colce’s limp. Their further adventures will include being locked out of their car, getting into a harrowing accident at a rural stop sign, visiting a church whose pastor prays over the men at Colce’s behest, and—most implausibly of all—not only attending a wealthy parishioner’s birthday party, where Cheaver has a comic sexual romp, but also encountering a tornado that has a therapeutic effect on TK’s condition.

Actually, this makes the picture sound far more energetic than it actually is, because despite all the incident it’s flatly written and played rather lackadaisically. Burger seems to be going for a dryly naturalistic style in which even outrageous moments—like that farcical sex scene Cheaver has on a lark—aren’t given much shape or panache and the more dramatic (or melodramatic) ones are tamped down as well. The result is a strangely undernourished mixture of the serious and the quirky, which unsuccessfully tries to merge a sympathetic picture of soldiers trying to reconnect with civilian life with a comic road trip.

The performances are similarly drained of vitality. Robbins—whom one might think a strange choice to star in a picture that ultimately seems to say little beyond “support the troops” anyway—mostly looks lethargic and vaguely disinterested, while McAdams’ lower-class spunkiness too often comes across as calculated. Pena’s character actually develops more than the others, and he catches the changes fairly subtly, though the turn in the last act is overly cute. This is basically a three-person piece, which is probably a good thing given that the rest of the cast are rather amateurish (or perhaps just indifferently directed)—though John Heard does show up for what amounts to a cameo in which he manages to chew the scenery for sixty seconds or so.

Undistinguished technically as well as narratively, “The Lucky Ones” is probably a sincere effort on Burger’s part to say something insightful about the soldiers coming back damaged from Iraq. But it represents a steep decline from the moodily effective “Illusionist” (and even from his earlier picture, “Interview with the Assassin”). Given the result, the title certainly doesn’t refer to the audience.