The debut directorial outing by Tommy Lee Jones, The Three Burials of Melquiades Estrada, may remind viewers of various works by thesps-turned-helmers like Marlon Brando, Clint Eastwood and Sean Penn. But the film it most reminded me of was Billy Bob Thornton’s All the Pretty Horses (2000, based on Cormac McCarthy’s novel). Both movies concern latter-day American cowboys who venture into Mexico.

Both are earnest, fastidiously crafted and persuasively atmospheric. Yet both, alas, end up as overlong, ungainly attempts to resuscitate the western.

In the film’s press notes, Jones cites as influences the works of Akira Kurosawa, Sam Peckinpah and Jean-Luc Godard. Leaving aside the inevitable whiff of pretension in that statement–and the fact that Godard’s cerebral oeuvre seems a million miles from Tommy Lee’s Texas (was he tripping when he saw Pierrot le Fou at Harvard?)–these models do bid us to recognize that, in films that deserve to be called works of art, the role of the director goes beyond determining camera positions and coaching actors. It also involves a comprehensive vision that welds material and medium into a unified, integral whole.

Lacking that, you can easily wind up with something that an actor rather than an auteur might assemble: a string of scenes, moments and ideas that feel, at best, loosely or arbitrarily connected. Three Burials has that aura of essential haphazardness; watching it, you’re too often tempted to second-guess the moment-by-moment artistic decisions being made in front of you. That’s a tough fault for any film to overcome, but it’s very possible that Jones’ limits as a filmmaker shouldn’t get all of the blame for it. There’s also his screenwriter to consider.

Guillermo Arriaga is the Mexican novelist turned screenwriter who gained international attention with his script for Alejandro González Iñárritu’s Amores Perros (2000). Reportedly, Jones admired that film and invited Arriaga to visit his West Texas ranch. The two men became friends, one thing led to another, and the next thing you know, Arriaga had been commissioned to write a script that’s not only a tribute to an American-Mexican friendship somewhat like his and Jones’, but that also stems from an incident that had stuck in Tommy Lee’s craw.

Since you won’t learn anything about that motivating event by watching Three Burials, permit me a brief mention of it. On May 20, 1997, a Texas high school student named Esequiel Hernandez Jr. was tending his family’s goats near the Rio Grande. The film’s press kit continues: “He knew the river … he didn’t know that his own government had posted four heavily armed, fully camouflaged Marines a few hundred yards from his family’s home. They had been sent to his Texas town on a counter drug mission, yet instead of surveilling smugglers, the Marines stalked this innocent youngster for almost half an hour and, after receiving radio approval from their commanders, shot and killed Zeke ‘in self-defense’ at a distance of 150 yards.”

This murder has been called the first killing of an American citizen by a U.S. soldier since Kent State in 1970. (No one was ever charged with the crime; the government offered Hernandez’ family a monetary settlement.) Understandably, Jones was outraged by the incident enough to want to say something about it. Understandably, in a different way, Esequiel and the particulars of his case had evaporated by the time Jones and Arriaga finished converting their real-life inspiration into movie fiction.

In their version, Melquiades Estrada (Julio Cesar Cedillo) is a gentle, stoic rancher who’s been a resident in Texas for some years. One day he turns up dead, shot in the chest by a high-powered rifle and stuffed in a shallow grave. After learning of the death, Texas rancher Pete Perkins (Jones) discovers that his friend was gunned down without provocation by a green Border Patrol officer named Mike Norton (Barry Pepper). Recalling his promise to Estrada to return his body to his Mexican village if he died in the United States, Perkins grabs Norton and forces him to dig up “Mel,” then accompany him on an arduous horseback journey across the Rio Grande, rotting corpse in tow.

Arriaga’s screenplay for Amores Perros contained a great deal of compelling surface energy and grit along with a tricky, Tarantino-like use of scrambled chronology, a device that further devolved into annoying mannerism in his and Iñárritu’s next film, 21 Grams (where the narrative logic seemed to be: If you have a boring story, try jumbling the time sequence so thoroughly that the audience will be so busy figuring out what’s going on that it won’t have the chance to realize how banal the material is). Three Burials starts out in much the same mode, opening with the discovery of Estrada’s corpse, then hopscotching backward in time to sketch the prior relationships of the main characters, and forward to follow Perkins’ initial reactions to the crime. Thankfully, once the rancher sets off on his morbid odyssey, the time-shifting ceases and we’re treated to a fairly straightforward story.

That odyssey, which occupies the film’s second half, is its most engaging section thanks to the combination of narrative directness and another virtue: the setting. Jones lives in these parts (sections of the film were shot on his ranch) and obviously has a deep feeling for the area’s mix of cultures and peoples, as well as for the stark beauty and fierce, unpredictable extremes of the landscape. Together with ace British cinematographer Chris Menges, he does a good job evoking the rocky fastness and hot, arid isolation of this section of the U.S.-Mexican border country (the film, however, was shot entirely in the United States, so parts of Texas stand in for Mexico in the story’s climactic section).

If only the film were as sharp with character as it is with topography. Although the thought didn’t occur while watching Three Burials, I later listened to a critic friend deride the movie for what he called an insufferable political correctness whereby all the Mexicans are saintly and sentimentalized while most of the Americans are odious and grotesque; besides the brutal, Hustler-addicted Norton, the gringos include Norton’s empty-headed wife (January Jones), a waitress (Melissa Leo) who seems to sleep with every man in town except her husband, and a stereotypically venal U.S. lawman (Dwight Yoakam).

Such deficiencies may well result from the reflexive P.C. simple-mindedness that seems to infect nine-tenths of those current movies (see The Constant Gardener; Syriana; Brokeback Mountain; Crash; Good Night, and Good Luck; etc.) that have any kind of political dimension. Yet you could blame it simply on lame writing. Certainly, Three Burials wilts in comparison to its most obvious model, Sam Peckinpah’s Bring Me the Head of Alfredo Garcia. In Peckinpah’s desperate, dust-choked realm, mortal corruption and the thirst for revenge are universal and inexorable; political pieties provide no leavening. At once moral, psychological and social, this vision has both poetic precision and metaphysical reach; to witness it now is to wonder at how tepid and superficial most of today’s films are in comparison.

It should be noted that while Jones is a terrific actor when working under a good director, his own directorial skills with actors prove notably uneven. Besides Cedillo, whose work as Estrada is appealingly understated, the most compelling performances come from Pepper and Jones as the Nortons. Though the characters may be cartoons, the young actors bring them to life with impressive skill and conviction. Less successful, meanwhile, are Leo and Yoakam, who surrender to the temptation to paint their characters in the broadest of strokes; this sacrifices all subtlety even as it points out the script’s creation of people who are more walking clichés than recognizable humans.

Directing himself, Jones displays a soft hand. To begin with, his character evidences an uncomfortable mix of posturing toughness and down-home nobility–as if the filmmaker were dying to play a badass, but a nice one. So the character is neither very interesting nor wholly believable. Late in the film, Jones seems to notice that and he gives Pete a scene where he’s in a Mexican cantina talking on the phone to that slutty waitress back in Texas, and he breaks down, telling her he loves her.

Since nothing we’ve seen before in the movie suggests that he actually does love her, the confession comes off like one of those scenes where an actor-director simply can’t resist giving himself a big emotional moment, credible or not. And that leaves us facing something we really don’t want to encounter in our cowboys: shameless self-indulgence.