“Trey, please,” said Helen Linsell, the dance director.

It was noon. Seven hours to go until they would be on stage, and not just any stage, but the prestigious Riley Theater in Leeds.

Of the 24 teenagers who had started rehearsals in June, 18 had made it to August. But the mood in the studio was edgy. The day before they had almost lost four dancers, including Trey. A lanky 17-year-old who likes to call himself the Bob Marley of the group, he had turned up late, rolling in at 11 a.m. Shannon, the girl with the curfew monitor on one ankle and the “Mum” tattoo on a foot, lost her temper. Parts were redistributed. There were tears and insults and very nearly a fight.

This is no ordinary dance company. The young people at Dance United have a background in trouble, not ballet. School dropouts and petty — and not so petty — criminals, they have been, as one youth worker put it, “sentenced to dance.” Referred by schools, parents and more often youth services, they train six hours a day for six weeks with professional contemporary coaches in a highly disciplined dance boot camp.

There is a 14-year-old girl at risk of sexual exploitation in her housing estate; a boy whose voice has barely broken but whose girlfriend just had an abortion; there is Trey’s girlfriend, Ellie (they started dating the second week). Tall and cheerful with raven-black hair pulled back in a messy bun, she is perhaps the most gifted dancer in the group. But a few weeks ago her mother kicked her out of the house and now she is, in her own words, “drifting.” (In line with a statute on the protection of minor offenders, none of them can be identified with their full names.)

Trey, Shannon and many others have been in and out of courtrooms. But nobody talks about it here. Not even the staff members know their histories. They deliberately choose not to.

“Giving them a clean slate is fundamental to our philosophy,” said Duncan Bedson, the manager of the Leeds project. “We can’t be prejudiced. For six weeks, they are dancers, period.”

Many cannot take the rigorous schedule. In week three this year they lost Georgia, who was so angry she punched a wall and hurt her hand so badly she had to go to the hospital. They lost Billie-Jo, who said on her first day in the studio that she was excited about “being happy for once.”

But those who stick with it get a chance to perform in a professional theater. And, as the experience of 36 Dance United academies in Leeds, Bradford, Wessex and London over the past seven years suggests, they also have a good chance of going back to school or finding jobs.

On average, 7 in 10 make it onto the stage; of those, 8 in 10 return to mainstream education or work, and more than 3 in 4 do not commit offenses or become repeat offenders. One in 10 even goes on to study dance professionally, with one Dance United graduate, Matthew-Jay Pratt, now in his final year at the competitive Trinity Laban Conservatoire of Music & Dance in London.

It is one of the most original and successful youth engagement programs in Britain, costing its private and public backers about $3,000 per person but saving society an estimated $128,000 in legal costs and welfare benefits, according to New Philanthropy Capital, a research firm that calculates returns for donors to charity.

On a Thursday in July, about halfway through the Leeds academy, the students were in the studio going over a tricky lift. It was Shannon’s turn.

Big Luke danced across the diagonal and grabbed Shannon’s waist, trying to turn her upside down and swivel her around, but her legs refused to go into the spinning wheel.

She stumbled. “I can’t do it, man.”

“Yes, you can,” Ms. Linsell said. “Come on, let’s try again.”

In his north London office, Rob Lynden, acting chief executive and creative director of Dance United, spoke of the transformative power of dance.

“We try to push, push, push the young people to an uncomfortable place,” he said. “We expect nothing less than what they can give. Because we know when they exceed their own expectations and that of others, they change.”

Dance United started out in the 1990s, working with Ethiopian street children, youths in post-reunification Germany and young Catholics and Protestants in Northern Ireland.

But in these times of economic hardship and austerity there is plenty of work to be done in England, particularly in the job-starved north, where the number of those under 24 who are neither employed nor in school has reached southern European levels, at nearly one in five.

Ask Trey what he has learned and he eagerly shows off his favorite move: a long sideways jump, his face and chest turned skyward and his arms wide open.

But he has also learned about getting up in the morning, even when his mother is still asleep, and how to follow a healthy diet. The dancers eat cereal for breakfast and tofu Bolognese for lunch. Soda is banned; there is water and juice.

And Trey has learned about books and the power to take control of your own story.

The show is called “Rewritten Pages.” It is about shedding labels and reshaping one’s life. Few of the teenagers had been read to as children, let alone read much themselves, except text messages and Facebook. But they know the power of words, of labels, first hand.

When the lights went out in the Riley Theater on Aug. 1, and the chatter in the audience subsided, 18 young dancers took the stage. Trey flew like an eagle and Shannon was suspended in midair, her legs tracing a perfect halo in the spotlight above.

Later, as the restless guitar music gave way to the sound of a heartbeat, she spun around and ripped two pages out of a book, discarding them calmly on the floor. Then she faced the audience, her gaze steady and her hazel eyes proud.