Even though Bill Pullman is an excellent horseman and owns a ranch, “The Ballad of Lefty Brown” is one of the rare Western-themed films in his long list of films and TV projects. With the exception of “Wyatt Earp” in 1994 and the 2000 television movie “The Virginian,” Pullman admitted Hollywood “doesn’t seem to think of me that way, just because of the roles I get offered. They seem to see me as the effete WASP guy, or the guy they need to play the president or some other politician,” as we’ve seen Pullman portray in such things as the two “Independence Day” films, the “1600 Penn” TV series, “LBJ” (in which he plays Texas Sen. Ralph Yarborough) or the upcoming “Backseat” film about Dick Cheney, in which he’s cast as former Vice President Nelson Rockefeller.

“Besides that, I also get those roles where I appear to be the nice guy on the outside at the beginning, but underneath maybe not so nice?” added Pullman. However, when he learned writer-director Jared Moshe was insistent on wanting him for “Lefty Brown” (opening Friday), Pullman was thrilled. “He got the fact that I could play this guy.”

This guy is Lefty Brown, a laid-back cowboy in the Old West who’s always been the sidekick and something of a court jester to a good friend (Peter Fonda) newly elected to the U.S. Senate. A horrible crime sends Brown on a journey to seek justice.

Joining Pullman for the interview, Moshe pointed out that having observed Pullman over the years, he was convinced he “had the versatility as an actor to make the transformation that Lefty had to make as a character. He could go from someone who no one takes seriously and become a guy who finds the power and the hero within himself by the end of the story.”

For Pullman, the biggest challenge of playing all that was tied to how movies are made. “As you know, they are usually shot out of order. Since I was playing a fellow who was changing so much as this went along, I had to constantly be aware of exactly where he was in each scene — and not play the early Lefty if we were shooting a scene that was going to be closer to the end of the movie.”

That said, Pullman did confirm that playing a totally fictional character like Lefty Brown “was a total delight. I’ve played so many real people recently — like Jack Kramer in ‘Battle of the Sexes,’ Ralph Yarborough in ‘LBJ,’ Jamie Dimon in ‘Too Big to Fail’ — it was wonderful to not have to worry about dealing with the issues you face when you play a real guy.

“Frankly, I didn’t want to do this Cheney movie — playing Rockefeller — and didn’t even want to talk to [director] Adam McKay, because I like him and I knew he’d talk me into doing it. Of course, I did and he did! … But that’s it. No more real people for a while!”