Remember Emmet Otter and His Jug Band? They’re Back, and Onstage.

Paul Williams — yes, that Paul Williams, the rare singer-songwriter to have collaborated with Barbra Streisand, Brian De Palma and Daft Punk — only had a few tips during a rehearsal back in November, but when he spoke, everybody listened. The squirrels, who had been quite rambunctious seconds earlier, focused. George and Melissa Rabbit were all ears.

After all, when the guy who wrote the score gives out notes, even woodland animals pay attention.

Williams, spry and impish at 81, had dropped by the New Victory Theater in Manhattan to check on the early stages of “Jim Henson’s Emmet Otter’s Jug-Band Christmas,” which boasts an onstage menagerie of puppets from Jim Henson’s Creature Shop.

Williams and Henson went way back, of course: In 1976, the musician was a guest on the eighth episode of “The Muppet Show,” and a few years later he wrote or co-wrote the songs for “The Muppet Movie,” including the Academy Award-nominated “Rainbow Connection.”

In between these two projects, Henson asked him to come up with the score for “Emmet Otter’s Jug-Band Christmas,” an hourlong TV special that aired in America on HBO in 1978.

“I was just thrilled to work with Jim,” Williams said. “He sent me the script and the book, and I just sat there and wrote. I think I was kind of being auditioned for ‘The Muppet Movie,’ which was a huge risk for them at the time.”

Based on an illustrated children’s book by Lillian and Russell Hoban, “Emmet Otter’s Jug-Band Christmas” starts off with the title character and his mother barely making ends meet by doing small jobs by the river in Frogtown Hollow. So when they hear of a talent show with a $50 cash prize, they separately decide to enter. Emmet plays the washtub bass in a group with his furry friends, and Ma sings, but they face stiff competition, especially from the naughty Riverbottom Nightmare Band, whose members include a stoat, a snake and a weasel. The 75-minute musical production runs Dec. 11-Jan. 2 at the New Victory, with streaming available Dec. 17-Jan. 2.

“What I love about the show, and really appreciate more now that I’m older, is that it has so much heart,” said Christopher Gattelli, who is directing and wrote the book with Timothy Allen McDonald. “At the same time it has that great Muppet madcap wit, those zingers and those really fast takes, and those 30-second acts that are just hilarious. It’s like a ‘Muppet Show’ with a story.”

Gattelli and McDonald worked on a first adaptation for Connecticut’s Goodspeed Musicals in 2008, but they went back to the drawing board for this one, which features four puppeteers and eight actors. “There’s more puppet business going on, and that’s music to my ear,” said Cheryl Henson, Jim’s daughter and an investor in the new show. (John Tartaglia, a Tony nominee for “Avenue Q,” is credited for puppet direction.)

While Goodspeed used some original figures from the special, they are now in museums and had to be rebuilt for the New Victory.

“But of course they don’t make the same fur anymore,” said Rollie Krewson, who built Wendell Porcupine and Charlie Beaver for the TV show; she is now a master puppet designer and builder at the Creature Shop. “I had to find furs that mimic more what the Emmet actor is wearing. They also wanted a new Ma, and we built a Pa Otter — there had never been one.”

During that rehearsal in Long Island City, the felt cast often behaved as if it had a life of its own in between scenes. “I consider it a good run if I forget they’re puppets,” Colin Trudell, who plays Emmet, said of his co-stars. “The puppeteers are also improv masters — the things that come out of their mouths in rehearsal really bring the characters alive.”

Trudell, who graduated from Texas State University in May, had not seen the TV show when he auditioned for the stage version, and he watched it for the first time before his callback. You can’t blame him for missing out: “Emmet Otter” stayed under the radar for a long time (it is now available for streaming on Amazon and other platforms); and a proper soundtrack did not come out until 2018, so it does not have the following of more famous Henson properties.

Its fans, however, are dedicated and loyal, often passing on the “Emmet Otter” tradition from one generation to the next, as happened in Gattelli’s family.

A big reason for the show’s cult following is its rare humor and warmth. Without getting preachy, it’s an ode to friendship and family bonds, as well as the idea of community. Sure, you won’t be able to get the song’s riff from your head after hearing the Riverbottom Nightmare Band snarl, “We take what we want/We do anything that we wish/We got no respect/For animal, birdy or fish.”

But it’s Ma Otter’s words you’ll remember: “Some say our world is getting too small,” she sings, “I say, with kindness,/There’s room for us all.”

Williams’s numbers for the original show offer an uncanny mélange of 1970s styles, with echoes of Randy Newman, Alice Cooper and the Carpenters. Except when the rollicking Nightmare Band pipes up, the music is filtered through a rootsy Americana vibe that transcends the decades, and was beautifully captured by My Morning Jacket in an aching cover of “Brothers in Our World” on the tribute “Muppets: The Green Album.”

“To me, the music is the heart and the soul of this piece,” Henson said. “What works so well is that it’s delivered by these characters that are creatures — it’s a living storybook.”

For Williams, those creatures made the assignment feel effortless: He just got the show’s furry (or scaly, as the case may be) subjects.

“There are all these little touches in the script, amazing little clues to who the characters are,” he said. “My wife and I use the line all the time when the Riverbottom Nightmare Band has just been totally rude to all the guys in the tree house, and Charlie says, ‘They seem nice.’ It’s that human element that speaks to me,” he continued, “and it speaks to me at a level where it’s the easiest writing I ever get to do.”

One thing that did not fit, though, is a conventional, “Jingle Bells”-type number. Though the story takes place around Christmas, there’s no song specifically about the holiday. Williams just did not see a need for it in “Emmet Otter.”

“There are two tasks in writing songs for a film or a stage play or whatever,” he said. “One is to illustrate the inner life of the character, and the other one is to advance the story. When you’re done, you go, ‘What’s missing?’ And it never felt like anything was missing.”