I've never been to Texas, but it can't get much less inviting than the border town in The Three Burials of Melquiades Estrada. The directorial debut from Tommy Lee Jones, best known as the special agent from Men In Black, depicts life in small-town Texas as dumb, dusty, and deadening, a transient place where people live in mobile homes and the primary diversion is casual adultery in motel rooms.

This is the starting point for a strange journey, in which a gruff cowboy called Pete Perkins (Tommy Lee Jones in great form) honours a promise to a dead friend, by taking his body back across the border to his family in Mexico.

The film opens in the desert of West Texas with the discovery of the corpse being chewed on by a coyote. The story, penned by Guillermo Arriaga (21 Grams, Ameros Perros), moves back and forth in time, showing how a strong bond develops between the grizzled foreman and the young Mexican Melquiades who he takes on as a herd on his cattle ranch, a friendship that bridges the divide set by prejudice and racism.

Mike Norton (Barry Pepper), a rookie border patrolman, is a stark contrast to the gentle Melquiades. We see Mike break a young Mexican girl's nose when she runs away from him while chasing down "illegals" ("You were way overboard there, boy," his superior tells him) and he treats his miserably bored wife (January Jones) like dirt. It is while he is masturbating among the desert scrub over a copy of Hustler that the patrolman responds to the sound of gunfire by mistakenly shooting the hapless Melquiades as he tends his goats. The episode was inspired by a real-life incident where US marines shot an innocent 18-year-old Texan, Esequiel Hernandez Jr in 1997.

Pete, enraged by the local sheriff's unwillingness to act on his friend's death (the Sheriff's excuse is Melquiades was a "wetback," although he knows who committed the crime), takes matters into his own hands. Pete kidnaps the guilty patrolman and forces him to exhume the body at gunpoint. Captor and hostage then begin a quixotic journey across desert mountains, with the rotting body slung over a mule. For both men, the journey is inward as well, taking on a mythic quality as Mike's past cruelties and callousness come back to visit him.

Jones makes an unpredictable avenging angel. A man who drawls few words, he is single-minded to the point of deranged in pursuit of his goal. Much of the power of Jones's fiery performance is that while he warms to the Mexicans they encounter on their journey, you are never sure how far the brooding Pete is prepared to go in dispensing his rough justice. He seems to carry the righteous anger of all abused border-country Mexicans on his shoulders.

Weirdness is not in short supply here, as the borders of acceptability are crossed. Moments of grotesque comedy, whenever the decomposing stiff moves centre stage, are offset by elements of Dukes of Hazard type idiocy as the cops in hot pursuit slip on banana skins. However, it is the undercurrent of melancholy sadness that suffuses the film, a tone that seems eloquently enhanced by the stark, arid landscape, with its occasional ramshackle buildings and run-down Mexican towns. One scene, in particular, where the two men meet a blind hermit (played by drummer Levon Helm of The Band) who feeds the men and then makes a parting request, is haunting in its simplicity. It forces Pete to question just how far he is prepared to go. For the audience though, he probably crossed the mark long ago.