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Having mastered Haberman’s choreography at the Church of St. Paul the Apostle (top), the Rockettes take it to Radio City for tech rehearsals (bottom).

Haberman began working on NYAC in April; two months later, she set up a workshop with 24 Rockettes, which allowed her to see the rough picture onstage, complete with a life-size bus. “When we first started learning the travel section, we were sitting on little chairs and cubes pretending we were on the upper deck of the bus,” Keeler recalls. “When we actually got on it, we had to make adjustments—how your arms could move in and out of the railing and dealing with the stairs and the windows.”

With Haberman in charge, the lost art of precision dance suddenly has a shot at rebirth. After studying at the School of American Ballet, she became entranced with Broadway and specifically Bob Fosse—her choreography, without sacrificing any of the Rockettes’ finely honed attack, recalls his humor, feminine power and sexiness. With the show’s other new number, Let Christmas Shine, Haberman transports precision dance to a sophisticated place. In one moment, a single Rockette appears, and then the rest gradually fill in the space, moving more lyrically than usual as the music builds, until all 36 are present—proving that their strength is as a group.

Because of Haberman, the Rockettes now offer some of the finest dancing to be found in New York—certainly surpassing what’s on Broadway. “Someone will come up to me at a ballet class and ask, ‘You’re a Rockette? I hear they’re doing really great things now,’ ” Keeler says. “Before, you’d get this reaction like, ‘Oh.’ ” She laughs. “Now I think of the Rockettes as a dance company. We’re not a troupe or a group or a team. We are a company and we work like one.”When the curtain finally comes down, Haberman will project stars from the Nativity over the entire theater. “I want the audience to feel like it’s encompassed by the whole universe,” she says. “And then my singers come back out and do this version of ‘Joy to the World’ that’s going to make you want to stand up and clap your hands. They lead us to the curtain, which rises.” She hesitates, and her face blossoms into a victorious smile. “I’m going to do real curtain calls. I understand it’s never been done.”

Radio City Christmas Spectacular runs through Dec 30 at Radio City Music Hall.