Good satire is sufficiently rare in today’s American film that you go to a movie like “The Men Who Stare at Goats” with high hopes. Unfortunately, they’re dashed again. This is a picture with a premise that, if treated with a sure touch and a bit of inspiration, might have been a wicked delight. Instead it offers just a few moderately amusing moments, and by and large proves curiously flat, despite all the talent on the screen.

The script, adapted by Peter Straughan from a book by Jon Ronson, deals with an eighties-era military program to develop the psychic powers of select recruits to form a brigade of mind warriors. But it backs into the story by focusing first on a contemporary small-time newspaper reporter, Bob Wilton (Ewan McGregor), who’s assigned to interview purported psychic Gus Lacey (Stephen Root), whom he dismisses as a crank. But he’s still fascinated by Lacey’s tales of the army’s psychic company, and especially its most mentally advanced—though rather loopy—member, Lyn Cassady, who was the only guy who could kill a goat just by staring at it.

Coincidence intervenes when Wilton, depressed after being dumped by his wife, goes off to Iraq as a war correspondent at the beginning of the 2003 invasion, only to bump into Cassady (George Clooney), who claims to have been recalled to service for a special mission inside the war zone. And because Cassady sees the makings of what he calls a Jedi in McGregor (a nice inside joke), he takes him along.

What follows is a two-track scenario. One, related in flashback by Wilton based on Cassady’s memories, tells the story of the creation of the so-called New Age Army by hippie-like Vietnam veteran Bill Django (Jeff Bridges) and Cassady’s emergence as his prime pupil. But the NEA’s sense of happy, sometimes drug-fueled camaraderie is undermined by the arrival of a new recruit, ambitious, arrogant faker Larry Hooper (Kevin Spacey), whose envy of Cassady’s abilities leads him to destroy the unit.

While that part of the story’s being told piecemeal, Cassady and Wilton continue their journey into Iraq, having what are supposed to be acidly funny adventures along the way—one involving a greedy American businessman (Robert Patrick) traveling with a pack of inept Blackwater-style bodyguards, another a group of kidnappers and their Iraqi victim (Waleed Zuaiter). The humor throughout is meant to be driven by Clooney’s wild-eyed certitude and McGregor’s incredulity over having allowed himself to be dragged into danger by such an apparent crackpot, and both men extract a few chuckles from the material by sheer force of will.

But for the most part the picture feels uneasily balanced between the semi-serious and the goofily comedic. It doesn’t have the guts—or the skill—to go whole hog the way that Kubrick did with “Dr. Strangelove,” surely the touchstone in this sort of film. (The closest it comes is in the caricature of the crazy general that Stephen Lang manages as the fellow who authorizes Django’s unit.) It doesn’t even reach the level of a less exalted, but still biting, satire like “Wag the Dog.” Instead it comes across as a feeble joke, rather like Mike Nichols’ bloated, clumsy adaptation of “Catch 22” did back in 1970.

That’s the case even when Bridges and Spacey return for the last act at a psych-ops camp deep in the desert. Even earlier on, Bridges had been doing little more than a repeat of his spaced-out “Big Lebowski” persona, and he merely brings it down a notch as an older version of the same. As for Spacey, he can’t add a slice of humor to a character for which the script provides none; his Hooper is no funnier than his Lex Luthor, who wasn’t really supposed to be. Like Clooney and McGregor, Patrick and Root try hard to generate amusement, but they have little to work with.

The fault must be laid, though, not on the cast, who do the best they can, but with Straughan’s script, which never takes Ronson’s book into the truly zany realm that Kubrick did with Peter George’s, and the oddly tentative direction by Grant Heslov, who never really allows the actors to cut loose. On the other hand, the picture looks fine. Robert Elswit’s widescreen cinematography revels in the wide desert vistas, and Rolfe Kent’s score tries to up the energy level.

But “The Men Who Stare at Goats” turns out to be a reflection of its title—odd, but finally bland.