“Uneasy lies the head that wears a crown,” Shakespeare wrote. But is that true when the coronet is no more than a backward ballcap balancing a pair of wraparound shades?

Such was the preferred headgear of Navy SEAL Chris Kyle, at least as portrayed by Bradley Cooper in “American Sniper,” Clint Eastwood’s respectful — if somewhat superficial — treatment of the real-life Kyle’s 2012 memoir of the same name. Kyle, who achieved renown as the most lethal sniper in American military history, with 160 confirmed kills and nearly 100 more unverified ones, was honored with the sobriquet “The Legend” during four tours of duty in Iraq.

On film, “American Sniper” treats him as a martyred hero. (In 2013, after leaving the service, Kyle was killed by a disturbed veteran whom he was mentoring.) And while that portrayal may arguably be justified, Cooper’s portrayal — while less than reverential — also reveals a man remarkably unburdened by conscience. When fellow SEAL Marc Lee (Luke Grimes) is killed during an ambush, and the dead man’s mother reads a letter from him at the funeral expressing doubts about the American military mission, Kyle remarks that it wasn’t a bullet that killed his friend but “that letter.”

Throughout the film, adapted for the screen by Jason Hall (“Paranoia”), Kyle comes across as a man gifted not just with the ability to shoot, but with a remarkable — and, at times, almost incomprehensible — moral clarity. Despite an opening scene that shows Kyle hesitating to pull the trigger on an Iraqi woman and a small boy who appear to be preparing to throw an antitank grenade at a convoy of Marines, “American Sniper” presents Kyle as someone with an almost superhuman ability to bear the same doubts that weigh so heavily on others in his job.

And make no mistake: “American Sniper” presents Kyle’s seemingly miraculous accomplishment as just that — something achieved while carrying out a task, albeit one of the most difficult and dangerous ones imaginable. Eastwood drives home this point again and again, showing us the bullet holes that appear in walls where SEALs and Marines have just been, only seconds earlier. Kyle, referred to as the “overwatch” and typically stationed on a rooftop to protect fighters on the ground, is a figurative cousin to Brad Pitt’s Wardaddy character in the film “Fury”: a surrogate father, keeping an eye on his “children” through the scope of a sniper rifle.

In the latest trailer for "American Sniper," directed by Clint Eastwood and based on the autobiography of the name, Bradley Cooper plays U.S. Navy SEAL sniper Chris Kyle, who is said to have had the most confirmed kills in U.S. military history. Kyle struggled with PTSD and was killed at a gun range by a fellow veteran in February 2013. The film opens Dec. 25. (Warner Bros. UK)

Of course, his real family, back in the United States, provides some contextual counterpoint to this slightly glorified interpretation. As Kyle’s wife (Sienna Miller) tells him, “It’s pretty egotistical to think you can protect us all.” Kyle’s buddy Lee puts it another way, wondering aloud whether Kyle has a “savior complex.”

For the most part, “American Sniper” is less interested in pursuing these and other questions of moral and psychological nuance than in telling a good war story. The main action follows two hunts: the first for a brutal lieutenant of al-Qaeda in Iraq leader Abu Musab al-Zarqawi, known as the “butcher of Fallujah” (Mido Hamada); and the second for a Syrian-born sniper and former Olympic sharpshooter nicknamed Mustafa (Sammy Sheik), whose own growing kill record taunts Kyle. Neither character figures prominently in the book, though both fictionalized versions here have been sharpened and enlarged in order to better delineate the peaks and valleys of the movie’s action.

From a narrative standpoint, it works. The battle scenes are alternately tense and thrilling, especially during one climactic sequence. Set during the approach of a massive sandstorm, it shows Kyle and his unit cornered on a rooftop by a mob of armed insurgents, while awaiting rescue by what is, essentially, the cavalry.

The flavor of a western is not accidental. Kyle, at one point, announces that he always wanted to be a cowboy. Maybe Eastwood does, too. Despite a couple of moments when it isn’t clear who the bad guys are and who the good guys are, “American Sniper” keeps its metaphorical headgear — white hats and blacks hats — very much separate.

★ ★ ★

R. At area theaters. Contains obscenity, sexual dialogue and violence, some of which is quite grisly. 132 minutes.