Screenwriter Guillermo Arriaga works in triads: the three episodes of Amores Perros, the three families of 21 Grams, and now the three—well, it’s right there in the title—of The Three Burials of Melquiades Estrada. The first of these films was set on the author’s home turf, in Mexico City, and the second in an unidentified American burg. The latest transpires on the border between the two countries, which is one of the reasons it’s the most interesting. Here, the thematic contrasts aren’t simply a matter of flashy structure.

That’s not to say Three Burials lacks a flashy structure. Melquiades Estrada (Julio César Cedillo) has already been buried once when the story begins: Ranch foreman Pete Perkins (Tommy Lee Jones) finds his body protruding halfway from a shallow grave, providing a meal for coyotes. Mel’s corpse has a bigger role than its living antecedent, but the Mexican migrant worker does have a few scenes that establish his friendship with Pete, the grizzled Texan who gives Estrada a job. (Pete is classically laconic, but bilingually so, his Spanish showing his empathy with the Mexicans he hires.) In a series of tightly clipped scenes, the film flashes back, forward, and all around, introducing its cast of characters and the circumstances of Mel’s death and subsequent interments. After that, however, the script untangles itself and becomes a road movie, traveling in a more or less direct line.

That trajectory suits Jones, who’s the director as well as the star. In his first big-screen feature, the veteran actor shows he can handle both Arriaga’s idiosyncrasies—which include casual violence, black humor, rough sex, and existential anxiety—and a knotty narrative. Yet Jones clearly aspires to something akin to a classic-Western vibe, which Three Burials achieves in its second half, when it becomes the tale of two men and a stiff pushing onward to fulfill a sacred duty. The mythic mood recalls John Ford and Sam Peckinpah, but it’s tempered by a sense of futility as contemporary as the soundtrack’s mix of Merle Haggard, Flaco Jimenez, and Chopin.

Because of his taste for fractured narrative, Arriaga’s scripts don’t build to a conventional climax. But they do tend to conceal aspects of their stories to boost dramatic impact, as Three Burials does for a time. Other than the scenes involving a still-breathing Mel, which clearly occur before the ones in which he’s dead, the early vignettes don’t announce their place in the chronology. What’s clear is that Pete wants justice for Mel, something that’s of considerably less interest to overeager Border Patrol Agent Mike Norton (Barry Pepper), who’s responsible for the first burial, and Sheriff Belmont (Dwight Yoakam), who orders the second. Neither cares what Pete thinks is the right thing to do, although that’s partly because of interpersonal distractions: Mike is feuding with model-thin wife Lou Ann (January Jones), who abhors the small-town existence to which his job has sentenced her, and Belmont hates Pete for sleeping with his lover, hard-faced waitress Rachel (Melissa Leo), who’s married to a third man.

Once Pete identifies Mel’s slayer as Mike—not information the movie withholds for long—the timeline basically stops twisting. Pete takes Mike to dig up Mel’s body and then cross the border to fulfill the promise Pete makes in the movie’s final flashback: to bury his Mexican pal in the hometown he described so affectionately. The trek won’t be easy, and it involves such stark encounters as one with a blind man (Levon Helm, Jones’ Coal Miner’s Daughter co-star, looking a bit cadaverous himself) who lives without friends, family, or hope. This is the straightforward part, though the film still includes a few circle games: Mike must rely on a woman he previously abused, and the two men come upon Mexican workers watching the same soap opera that played during one of the low points of Mike and Lou Ann’s marriage.

With a beguilingly relaxed rhythm and elegant cinematography by the great Chris Menges, Three Burials is a pleasure to watch. Yet the film does lack a critical dramatic element: any growth in Pete’s character. Road movies are supposed to lead someplace new, psychologically as well as geographically, but only the kidnapped Mike learns anything on the trek to Mexico. At the end, Pete is the same guy he was at the beginning: gruff, obstinate, and too principled to be constrained by the letter of the law. The Village Voice’s Michael Atkinson has gone so far as to compare the taciturn character to George W. Bush, a man who acts as if he’s proving himself correct whenever he refuses to say why he is. That’s probably not what Jones had in mind, but The Three Burials of Melquiades Estrada is nonetheless an ode to a righteous cowpoke whose determination borders on delusion.