Little Harriet plays with matches against her parents’ wishes and goes up in crackling flames. Cruel Frederick whips a dog unmercifully and is bitten to death. Silly Conrad can’t keep from sucking his thumbs, so the long-legged scissor man neatly snips them off. In Struwwelpeter (“Slovenly Peter”), Heinrich Hoffman’s 1844 book of cautionary tales for children, these naughty kids and others of their ilk inhabit a quaint world reminiscent of Monty Python’s and are punished in highly entertaining ways. The book is as popular in Germany as Alice in Wonderland is in Great Britain and the United States. But still, it’s not an obvious starting point for an opera — even for a so-called junk opera named Shockheaded Peter.

Shockheaded Peter is anything but obvious. Victorian puppets perform the action, and the morbid, whimsical music is provided by The Tiger Lillies, an English cult trio. Equally startling is the fact of the show’s success: After a much-praised opening in London two years ago, the odd musical melodrama is edging its way into the U.S. with a four-city tour. After playing the Kennedy Center, the production will move to Houston, where it’s sponsored by Society for the Performing Arts.

The show was born about four years ago, when Shockheaded producer Michael Morris introduced The Tiger Lillies’ Martyn Jacques to the book. Jacques is famous for his unearthly falsetto — “like Tom Waits on helium,” says Phelim McDermott, co-director of the production. Just as famous is Jacques’s unearthly sensibility: “Martyn is an extraordinary creature,” continues McDermott. “He is a bit of a freak and misfit.”

Eleven years ago, at age 29, Jacques gave up the operatic tenor roles his voice coaches had urged him to pursue. Instead, he began writing experimental songs for the accordion — and for the startling “high falsetto” voice he had begun to cultivate. Combining the accordion with countertenor, he says, “I felt I was producing something fairly original, fairly unique.” Conveniently, he was living above a strip joint in London’s Soho, and the din of marketers and tourists drowned out his less pleasant efforts.

Not surprisingly, Struwwelpeter appealed to Jacques, inspiring a song about Conrad, the thumb-sucker. On the phone with Morris, the producer, he played it on the ukulele. Morris asked him to write more.

Jacques admits that he exaggerated the already ludricrous tales. “It’s a little over the top,” he says proudly. “It’s a case where the crime doesn’t fit the punishment.” In the melodies, he managed to squeeze in a little chanson, Berlin-style cabaret sound, and a few German polka strains. Plus, he says, a little opera, blues and “gypsy singing.”

During the production, the musicians narrate each tale while suspended high above the stage, each inside a Hollywood Squares-style cubicle. On the stage, garish-faced actors in Victorian garb recreate 19 storybook characters through pantomime and puppetry. The gore is hardly the stuff of graphic movies: For instance, when the evil scissor man amputates the thumbs of stubborn Conrad, red handkerchiefs are dramatically pulled from the papier-mรขchรฉ puppet’s wrists as he “bleeds” to death.

“In order to create a show out of the poems, we’ve put the stories together like a Grimm’s Fairy Tale collection, like a traveling theater company with an emcee,” McDermott says. “The set doesn’t quite fit together, so it falls to the ground. The stories of children are presented like a freak show.” Instead of performing in front of large fixed sets and props, the actors operate everything themselves without relying on hydraulics. Co-director Julian Crouch designed the sets with the actors’ and musicians’ capabilities in mind. “We almost treat the set like a puppet,” McDermott says.

When the show debuted, he worried it might be too scary. It wasn’t. Although SPA doesn’t recommend the show for children under 14, McDermott says the liveliest audiences have included kids accompanied by their parents. In England, the opera has attracted a cult following among youngsters, punk rockers and older folk who grew up hearing Hoffman’s nonsensical tales — and none of them seem fazed by the puppets’ violence. “When the boy’s thumbs get cut off by the scissor man, the audience is shrieking with glee,” says McDermott.

But is North America ready for it?

“I’m not sure anyone’s ready for it,” he says.

Society for the Performing Arts presents Shockheaded Peter at the Wortham Center’s Cullen Theater Thursday through Saturday, October 7-9, at 8 p.m. For tickets, call (713)227-4772.