Cinderella’s carriage is made out of a dozen dancers in black holding simple props. (Angela Sterling/Dutch National Ballet)

A few San Francisco Ballet company members recently gave principal dancer Dores Andre a good scare. Between rehearsals for the troupe’s new production of “Cinderella,” the pranksters hid and jumped out at Andre, causing her to emit a glass-shattering scream.

“They were wearing all black and standing against a black wall, so I couldn’t see them,” Andre says. “They got me so bad.”

It was a good prank and also good practice for dancing in choreographer Christopher Wheeldon’s “Cinderella,” which requires some of its performers to remain onstage but vanish from sight.

The production, which opens at the Kennedy Center on Wednesday, retains the classic ballet’s original score by Sergei Prokofiev, but Wheeldon — with an assist by pre-eminent puppeteer Basil Twist — has created a “Cinderella” that’s a little more down-to-earth than previous versions of the ballet. This production, co-commissioned by the Dutch National Ballet, still has plenty of magic, Twist says, but it’s decidedly low-tech — often requiring dancers to fade into the background and serve as ad hoc puppeteers.

“It’s a very peculiar thing to ask any dancer — but especially a ballet dancer — to do,” Twist says. “I actually trained the dancers to hide their amazing bodies and put their energy into something else.”

One object that the dancers bring to life is a magical tree, which sprouts from tears Cinderella sheds over her mother’s grave. Black-clad dancers manipulate the fabric sapling, making it twist and grow. Later, as a full-grown tree, it swallows Cinderella and spits her out in a beautiful golden gown and then sheds branches that assemble themselves into her stagecoach.

Replacing the fairy godmother with a tree gives this production of the fairy tale a modern twist, Twist says.

“Through Cinderella’s constant visits to the tree, it becomes bigger and stronger,” Twist says. “So then when it gives Cinderella her gown and her carriage, it’s less like these things are happening to her, and more like she’s made these things happen for herself.”

Andre, who will dance the role of Cinderella for two of the seven performances at the Kennedy Center, was skeptical when she first saw the tree from backstage. “It didn’t look like a tree at all. It just looked like a lot of fabric and panels,” she says.

Later, when Andre saw her fellow dancers bring the tree to life, she was astonished. “It is the most magical, beautiful thing. Now it’s one of my favorite parts of the ballet,” she says.

Andre approves of another of this production’s additions to the classic tale. Traditionally, Cinderella and her prince fall in love at first sight at the ball. In Wheeldon’s version, they meet earlier, when the prince (disguised as a messenger) arrives at Cinderella’s house, and our heroine asks him for dance lessons.

“You get to see them fall in love,” Andre says. “It’s a cute scene, and more believable.”

Also more believable are the stepsisters. In past versions of the ballet, the pair are cartoonishly mean and ugly, to the point of being danced by men in drag. In Wheeldon’s “Cinderella,” the stepsisters (played by women) have more realistic reasons for their bad behavior. One, who is physically beautiful but spiritually ugly, is driven by selfishness and an overweening mother. The other, who is plain-looking but kind, is forced into bullying Cinderella against her will.

“The nice stepsister ends up getting a love story of her own,” Andre adds. In fact, by the end of the ballet, the stage is filled with whirling couples as Prokofiev’s shimmering strings send them off to happily ever after.

In this way, Wheeldon’s “Cinderella” both hews to and broadens its fairy-tale mandate. You don’t have to be saintly and stunningly gorgeous to get your prince; average-looking and moderately nice girls get to find love, too.

Kennedy Center, 2700 F St. NW; Oct. 26-28, 7:30 p.m., Oct. 29 & 30, 1:30 & 7:30 p.m., $29-$139.

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