LOS ANGELES—To some people—journalists at a packed L.A. news conference, for instance—the correct placement of an eye patch is a big deal. In this case, the patch in question belongs to the iconic character Rooster Cogburn, of both Charles Portis’s 1968 western-adventure novel, True Grit, and the 1969 film for which John Wayne won an Oscar portraying the boozy, one-eyed U.S. marshal. In both the book (which would seem to be the authority) and the film, the patch was affixed over Cogburn’s left eye.

Historical precedents notwith-standing, for his single-peepered Rooster in Joel and Ethan Coen’s adaptation of True Grit, Jeff Bridges unapologetically patched things his way.

“Uh, you know, we put it on the right eye and it felt good. We put it on the left eye, uh, not so good. Put it on the right eye, uh, ”˜This feels right.’ Then, ”˜What do you think, guys?’ ” the ever laid-back actor—who, with his long, silvery hair and beard, looks much like his film character, except groomed and presumably clean—says, reenacting how he asked his writer-directors their opinion on the matter. “And then we went back and forth like that.” The black leather patch, needless to say, ended up covering the right eye, correctness be damned.

And in actual fact, the Coen brothers didn’t exactly note that their Rooster’s patch wasn’t over the same eye as his predecessors’. “We did talk about switching from eye to eye, scene to scene,” Ethan says, joking, “to see if anybody would notice.”

Before he even got to the accessorizing stage of True Grit’s whiskey-soaked, unwashed, trigger-happy Cogburn, Bridges (who’s also starring in Tron: Legacy) had a yet more burning question. Why, he wondered, did the brothers want to remake a famous, beloved movie that featured a towering performance by Wayne?

“I think it was Ethan I talked to first, and he corrected me and said, ”˜No, we’re not making that movie,’ ” Bridges recalls. “ ”˜We’re making the book.’ As if there wasn’t another movie ever made kind of thing. ”˜We’re just referring to the book.’ And I wasn’t familiar with the book, and he said, ”˜Well, check that out and tell me what you think.’ And I read the book, and then I saw what they were talking about, because it’s such a wonderful book. It suited them so well, I thought.”

He took the role. After all, things had gone swimmingly with the last film in which the Coens had directed him: their 1998 crime comedy The Big Lebowski, in which Bridges played filmdom’s notorious slacker hero the Dude. But in keeping with the brothers’ habit of doing about-faces with each new film, True Grit—although equipped with its own black-comic eccentricity—was worlds away from Lebowski’s land of weed, bathrobes, and bowling alleys.

In the story set in 1870s Arkansas, Cogburn reluctantly allows himself to be hired by feisty 14-year-old Mattie Ross (Hailee Steinfeld), who wants the “meanest” marshal around to help her hunt and bring to justice a man named Tom Chaney (Josh Brolin), who killed her father. When Texas Ranger LaBoeuf (Matt Damon) turns up on Chaney’s trail for a different murder, Cogburn and LaBoeuf team up and take off. Refusing to be left in the dust, Mattie follows, and the unlikely posse rides into Indian territory in the wicked winter. The three quibble and quarrel and Rooster occasionally gets ripped. They encounter bad men, bullets fly, and justice is pitiless.

Bridges’s garble-tongued (sometimes to the point of unintelligibility) Cogburn comes across rather like a pistol-packing synthesis of the Dude and Bad Blake, his down-and-out country singer in Crazy Heart, for which he won an Oscar. “God, what a great character. You know, most westerns have that strong, silent type, and here’s this boorish, you know, ”˜Brah, brah, brah,’ ” he says, mocking his decidedly loquacious lawman.

There was the small matter of the film’s climax, in which Cogburn faces down four outlaws. The scene required Bridges—an experienced rider—to gallop his horse forward while firing two big guns and holding the animal’s reins between his teeth. “I remember that day well,” he says. “Right in the beginning of the day, I remember Joel coming over to me and saying, ”˜What do you think about really trying this deal?’ And I said, ”˜Oh, all right. That’s kind of interesting, you know.’ A little anxious, a little fear, and then ride myself to, you know, do it in my teeth. And so we did it that way, and it wasn’t as tough as I thought, actually. It was kind of cool. You know, I had a horse that kept the rhythm well, and that’s basically it, from my point of view.”

Just one more thing: what does the man who can ride hard while holding his horse’s reins between his teeth think “true grit” is?

“Well, true grit—I believe this is my definition of it—is, uh, seeing one thing through to the end, you know. That’s a good thing. I aspire to that.”