Jarhead is the name Marines give themselves, supposedly because their round, shaved heads look like a jar top, though someone with a better sense of imagery might have chosen a different one (penis-head comes to mind). It's also the title of a powerful new film, written by William Broyles Jr. from the memoir by Anthony Swofford about his life from basic training through the bizarre days and nights of Desert Storm in 1991.

Directed by Sam Mendes (and how different this is from "American Beauty" and "Road to Perdition"), the film is a balls-out, take-no-prisoners look at a squad of Marine trainees as they slowly become the elite spotter-sniper teams that the American military believes are essential in wartime. The procedure to be followed is to brutalize and brutalize and brutalize again until the desired level of skill is attained. The men are cruel to each other, panicked about losing the girls/women they left behind - there is a "wall of shame" with photos and notes from the wives and girlfriends who've abandoned them - and a sickening porno video sent by a wife, to be shown to the whole squad, along with a little extra comment she makes: "Who's fucking around now?"

Jake Gyllenhaal is the sniper Tony Swofford, and Gyllenhaal shows his acting range here; he is a young man who hides his intellect (he reads Camus) while at the same time he becomes an expert at killing, at least in training. His spotter partner Troy is played by Peter Sarsgaard, who is a bit too much like Tony; they seem more like brothers than partners. Almost every moment of their lives in the squad is controlled by Staff Sgt. Sykes, in a wonderful performance by Jamie Foxx, who has made quite a journey from his days at "In Living Color," to "Ali," to "Ray," and now to "Jarhead."

Although the film lacks a conventional structure - the men trained to fight a war, were shipped to the Middle East where for months all they did was guard Saudi oil wells, and then found that Saddam Hussein's army had melted away when the war actually started - the film is brilliantly shot by Roger Deakins ("Shawshank Redemption," "Barton Fink") and edited by Walter Murch ("Apocalypse Now," "The English Patient"). The endless desert, lacking anything resembling a horizon line; the ghastly fires of the oil wells burning - and spilling black smoke over everything and everyone - all of it is so vivid we can taste and smell it.

There is occasional voiceover comment by Gyllenhaal as Swofford; describing the days' activities he tells us they mainly rely on masturbation, along with writing the occasional letter, eating, or just generally being bored. And when finally the chance comes for payback, for using the skills that cost so much in humiliation and brutality, for the actual invasion of Iraq and the chance for Swofford and Troy to be the sniper-spotter team and kill an Iraqi officer, their orders are countermanded in order that an air strike be used instead. The film has built up to this moment for so long, that when Troy breaks down in tears, we are completely with him; we also want to kill, kill, kill. Quite a film.