On Sunday morning, Frank Oz — the celebrated puppeteer behind such Jim Henson characters as Miss Piggy, Grover, Fozzie Bear, and Sam the Eagle — premieres his new documentary “Muppet Guys Talking: Secrets Behind the Show the Whole World Watched” at SXSW. The film is a candid, often bitingly funny conversation between Oz and four of his closest colleagues: Dave Goelz (Gonzo), Bill Barretta (Rowlf the Dog), Fran Brill (Little Bird), and Jerry Nelson (Count von Count), who died in 2012.

Oz, 72, started his career as a puppeteer when he met Jim Henson at 19, and he went on to become a successful director of such comedic hits as “What About Bob?,” “In and Out,” and “Bowfinger.” He got the idea for his latest movie from his wife, Victoria, a business consultant, who thought the close camaraderie he shared with his co-workers is rare — proof that business culture can still be fun.

Oz shot the conversation some years ago, and only got around to putting the final touches on it now. “The terrible thing is, I don’t rush when I don’t have a deadline,” he says. “We had no deadline.” Ahead of the film’s premiere, Oz spoke to Variety about the Muppets, why the ABC reboot TV series didn’t work in 2015, and if he’s really returning as Yoda in the new “Star Wars.”

As a lifelong Muppets fan, I enjoyed seeing all of you together. Do you have a favorite character that you’ve performed?
It’s like saying, “Who is your favorite kid?” They all have value to me. Piggy has had tremendous depth to her. Animal is very simple and crazy. I think the one that has felt the most organic to me when I did it was Grover.

Somehow there was a clear channel that went from a part of me to a part of Grover. We all have an essence of our characters. Sometimes one has an essence that’s a bit stronger.

How did you find Miss Piggy’s voice?
We create characters all different ways. My way is trial and error and playing with other people. One does not work in a vacuum. In order for my character to grow and have a voice, you need the other performances to work against. We basically played. As we played, I thought, “I’ll take something out and put something in.” Eventually the voice came about. It’s a process.

Was it inspired by a specific person?
No. I’d feel very sorry for that person.

Did you ever think that a woman should voice her?
It wasn’t the question of a woman or not. It was the question of who’s the funniest. If there was a woman who was as funny as me doing Piggy, then we would have traded off. It’s not about that. These characters came alive by some sort of joyous chemistry that Jim guided us on.

Were you surprised that Miss Piggy became a gay rights icon?
I was kind of aware of it. My job is to touch people with the characters. The fact that it touched a particular group that was in pain and somehow it was a comfort—I remember, during that time, there was women’s lib, too, and she was important there. It comes from the writers and Jim being a citizen of the world. If I was fortunate enough to help that community, all the better.

What’s the legacy of the Muppets?
It’s kind of not for me to say. All these years, I put my nose to the grindstone and worked. I guess the legacy is really Jim—having fun and doing work. That’s all that Jim wanted.

I wonder if kids growing up today appreciate how important the Muppets were to children from my generation, in the 80s.
No, I don’t think they do. I don’t think it’s right to expect them to do that. Each generation has its own significant performers. When kids or teenagers look at it now, it tends to hold up pretty well. But they don’t appreciate it the same way.

Did you see the new “The Muppets” TV show on ABC?
I did—the first 15 minutes.

Why did you stop?
I felt the show wasn’t true to the characters. There was a purity in each character that was vital. I felt that purity was being moved around to areas that didn’t feel right.

It was cancelled quickly.
My brothers, my sisters, were in there [as the puppeteers]. They did the very best they could. But essentially, they were working with scripts that other people wrote. They had to do it the way it was. If it was given more air and they trusted the performers, as we had air, it would have come alive more. Those abilities, to riff and be smart enough, weren’t appreciated.

What did you think of “Muppets Most Wanted,” the last movie released by Disney?
I think there were some very funny things individually. And the purity of certain characters stayed. I got to hand it to Disney—they tried. It’s very difficult. Disney and all these people are trying to do the right thing. It’s like you’re a fan of Formula One racing, you go to every race. But being a fan of it and driving it are different things. They are fans and they want to drive it as well; it’s not as easy as people think.

It’s been 10 years since you worked with the Muppets. Would you ever go back?
That depends. I was doing a couple days a few years ago at Sesame Street. I have not been asked, partly because I’m expensive. I worked a certain way; I work with the abandon that Jim taught me. I don’t know the young people at Sesame Street, so I don’t know what kind of fit I’d be. As far as working with the guys, I love working with them, but not all the time. I’m a director. I love directing. I miss my characters.

Was it hard to transition from being a puppeteer to a director?
When I joined working with Jim, I was 19. Jim always wanted to be in the beginning an experimental filmmaker, and that’s what he was, more than a puppeteer. I always wanted to be a director. It was an opportunity to learn. I gave myself 10 years to be a movie director. Whenever Jim was editing, I would be there. And then what happened, it was so extraordinary, Jim asked me to co-direct “The Dark Crystal.” I had never directed. It was vast. Then Jim asked me to direct “The Muppets Take Manhattan,” and then after that I was asked by David Geffen to do “Little Shop of Horrors.” I didn’t screw up, so they kept asking me.

There are reports that you might reprise Yoda in the new “Star Wars.”
I feel like I’m a prisoner at war here, and I can only give you my name, rank and serial number. To be true to the people who asked me, and they are kind of my family, I have to say I’ve been asked not to talk about it. I love Yoda. I would be happy to talk to you about it at the time they let me.

Do you see “Star Wars: Rogue One”?
I have not. I have my Academy DVD. Tell me something. How do people see everything?

But you did see “The Force Awakens”?
I thought J.J. Abrams did a great job of synthesizing all this information. It was a tough thing for J.J. to be asked to do—to transition to a new family of “Star Wars” and still pay homage and respect to the others. It’s different from the way that George Lucas would have done it. George would probably have had a more overall arch that would follow the other stories and have a moral depth. But, my gosh, what J.J. did was really entertaining. It was so much fun.