If you happened to be in the right place at the right time in New Orleans last week, you might have seen actor William Baldwin riding a bike down Royal Street, taking a break from shooting the psychological thriller “Cut Off.”

“There’s no other place like it on the planet,” said Baldwin of the Crescent City.

“But I’ve also been on the set quite a bit,” he added. That’s because although he had a small role, the independent, low-budget “Cut Off” is being filmed on a tight schedule — just four weeks.

The actor’s dozens of film and TV projects have included “Gossip Girl,” “Parenthood,” “The Squid and the Whale,” “Backdraft” and “Flatliners.”

In “Cut Off,” written and directed by local filmmaker Jowan Carbin, John Robinson (“Elephant,” “Lords of Dogtown”) stars as Clive Stone, a troubled man who struggles with his new life in New Orleans after his family relocates from Los Angeles.

The film also features Jean-Marc Barr (“Europa,” “The Big Blue”) and Oscar nominee Brad Dourif (“Blue Velvet,” “The Lord of the Rings.”)

Baldwin plays Haskel, a villainous-looking character whose body is covered with tattoos and scars. During some on-set improvisation, he introduced himself as “Haskel the rascal.”

But “he’s a sheep in wolf’s clothing,” Baldwin said. “He looks badass, but he’s got a heart of gold.”

Although “Cut Off” is Baldwin’s first filmmaking experience in Louisiana, he and his brother, Stephen, shot a commercial for Levi’s 501 jeans in the area in the mid-1980s. Between making the commercial and “Cut Off,” Baldwin, like millions of others, visited New Orleans for fun.

He managed to work some leisure into his schedule on this visit, too, dining at chef John Besh’s Lüke and the Ruby Slipper.

“I came in to play this fun little part, Haskel,” the actor said. “And I’m working with some really terrific actors. Brad Dourif is one of my favorites. He’s done some earth-shattering performances in his career.”

Baldwin praised “Cut Off” writer-director Corbin, too.

“He really is a terrific writer who completely gets this part of the world,” Baldwin said. “That comes oozing through in this movie. The way he wrote my character, it’s almost more like lyrics than dialogue.”

Unlike many movies in which New Orleans and Louisiana stand in for other places, “Cut Off” is set here. Local flavor informs the storytelling and characters.

“The stuff that my character says is woven into the culture,” Baldwin said. “Some of the dialogue that my character says is unlike anything I’ve said before.”

Co-star Jean-Marc Barr plays Trevor De Blanc, a Louisiana native who was a college professor in California before he returned to the state, just in time to experience Hurricane Katrina and the BP oil disaster.

The four-week production schedule for the independently produced “Cut Off,” which began March 14, is a challenge for everyone involved, the actors said.

“We’ve got three weeks to finish it,” Barr said. “It’s a real discipline. It’s commando.”

There’s no choice but to hustle, Baldwin said. “If you’re making a movie for $1.2 million, $1.5 million, you have to lay it all out, have it organized,” he said. “You don’t rehearse much. You don’t get as many takes. If you see Take 3, you’re lucky.”

Still, “Cut Off” is an unconventional project that both Baldwin and Barr are enjoying.

“This kind of film is a rarity in Hollywood,” Barr said. “It’s a film that is quite subversive in its plot and its emotion.”

That kind of alternative is satisfying for actors.

“The studios make fewer films, and a lot of it is Batman and Superman and ‘Mission Impossible,’ ” Baldwin said. “It isn’t stuff that interests me.”

Barr, an actor who does much film work in Europe, agrees.

“Billy and I are from the ’60s and ’70s,” he said. “We had films like ‘Easy Rider’ and ‘Taxi Driver,’ films that became cultural statements. This film is going to be entertaining in its way, but it’s also a cultural statement, putting a mirror on what’s happening in the country today.”