Actor Treat Williams calculates that he’s worked with more than a hundred directors over a 44-year acting career, and no one else approached a movie like Sidney Lumet.

Williams starred in Lumet’s 1981 film Prince of the City and now, five years after Lumet’s death, he’s recalling that experience in connection with By Sidney Lumet, an American Masters documentary airing Tuesday (January, 3) at 8 p.m., ET on PBS. (Check local listings.)

“I loved Sidney Lumet,” says Williams. “There are things I learned from him that I still take with me for every project I do.”

Lumet, who died in 2011 at the age of 85, amassed a film resume that included Dog Day Afternoon, Serpico, Murder on the Orient Express, Long Day’s Journey Into Night, 12 Angry Men, Network and The Verdict (with Paul Newman and Charlotte Rampling, right), among many others.

While Lumet’s films were noted for their social commentary, he insists in the American Masters documentary that he never set out to make statements.

“I just want to tell the story,” he says in a 2008 interview that comprises the major part of the documentary. “If I tell the story right, the rest of the message will come across.”

American Masters notes recurring themes in Lumet’s work, like the nature of justice and the value of one person standing up when it would have been easier to sit down. Cases in point: Henry Fonda’s character in 12 Angry Men and Al Pacino’s character in Serpico.

Or Williams’s character in Prince of the City, Danny Ciello, who exposes corruption in a more nuanced police world than the one Pacino’s Serpico exposed almost a decade earlier.

Williams attributes the depth of Prince in significant part to Lumet’s philosophy of groundwork.

“He came from a background of live television drama, where you had to have everything ready to go in one shot,” Williams notes. “So he believed in rehearsal.

“We rented a big place on Second Avenue and rehearsed for three weeks, which was unheard of. We did every scene. We did three complete run-throughs of the entire script, with the whole cast there for all of it.

“That was a different time, of course. Films shot in about 60 days. Now you get off the plane and go right to work. The whole shoot might run 12, 15 days.

“But all that rehearsal pays off. You got a sense of how he directed, how he saw the film, why this scene was in it.”

Interestingly, though, Williams adds, Lumet didn’t obsessively film a scene over and over once the cameras were rolling. 

“You have directors who make you do scenes dozens of times,” he says. “When Sidney got what he wanted, he’d just say, ‘That’s a print.’ I loved it.  

“Actors are always thinking they want one or two more, so you’d sometimes say, ‘Are you sure?’ And he’d say, ‘You want another one?’ And you’d say, ‘Well, if you liked it, I guess not.’ And he’d say okay, let’s move forward.”

Williams has worked over the years with directors like Steven Spielberg, Milos Forman, John Sturgess and Woody Allen. He puts Lumet in the first tier and says his experience is that directors, unlike actors, don’t tend to cluster into particular schools.

“They’re all pretty individual,” he says. “Maybe because they come from such different backgrounds.  Sidney was a child actor, so he really understood things from the actors’ perspective. He was a wonderful mentor.”

Williams got the Danny Ciello role after Lumet saw him on Broadway in Grease. Williams says he’d been hoping to work with Lumet for some time before that.

“Are you kidding?” he says. “I think I’d seen everything he did. 12 Angry Men, Serpico. These were the classics. Sidney and Martin Scorsese, who was also coming up at that time, were the directors that all us young actors wanted to work with.

Unlike some directors, Lumet never gathered a de facto repertory company of actors to whom he kept turning, and Williams says that also reflected one of his strengths.

“He was always looking for something new,” says Williams. “Look at the range of his work. One of my favorites is Murder on the Orient Express, which is totally different from, say, Dog Day Afternoon (Al Pacino with John Cazale, right, 1975.) They even require different styles of acting.

“If he liked a story, he’d say, ‘I’ll make a film about it. What are they going to do if it doesn’t work? Kill me?’ ”

Besides the value of rehearsal, Williams says he still employs other lessons he learned from Lumet.

“He taught me a lot about the camera,” he says, “like how little you have to do for it, in contrast to stage acting.

“If every director took Sidney’s approach, there’d be a lot more comfortable actors.”

And maybe more films about justice and humanity.