Gory stories, quirky music, clever puppets, staggering hilarity: Different people will find different reasons to adore “Shockheaded Peter.” This freewheeling adaptation of the “Struwwelpeter” tales, Heinrich Hoffmann’s cautionary lessons for naughty 19th-century children, won raves on its first trip from London five years ago. As it reopened last night at the Little Shubert, the show captivated me, for one, with ineptitude.

There is much to be said for badness, for the tonic properties of the really awful.

Directors Julian Crouch and Phelim McDermott, and the rest of the company that jointly created the piece, filter Hoffmann’s tales through the creaky conventions of Victorian fright theater. An emcee in top hat, tails, and stringy black wig promises us unspeakable horrors. “The revelation-shy amongst you are well advised to avert your eyes,” he warns, opening one door or another to introduce some dramatization of Hoffmann’s macabre stories.

See, for instance, the girl who played with matches, and was burned to a crisp. Or witness the boy who sucked his thumbs until a demon came and snip-snipped them off. Again and again, naughty kiddies meet some gruesome end. (Hoffmann was German, as if you couldn’t tell.) Often when the emcee flings open a door, it shows a member of the Tiger Lillies, the three-piece band that adds weird and delightful music to the evening. With his impossibly high voice and air of mild alarm, vocalist/accordionist Martyn Jacques sings as if he, too, has experienced a snip-snip.

But it is the emcee himself around whom the show revolves. Exceptionally lanky, swinging his walking stick this way and that, he might be a scarecrow in high stockings and scarf. You gather from his performance that he is a classically trained actor, but only because he tells you so.

Consider: When the show begins, the emcee twirls through a door and seems to make eye contact with everyone in the room. This is a standard feature in theatrical memoirs. People who have witnessed great actors are always writing that they felt Garrick or Kean or Olivier delivered a soliloquy directly to them, only to discover at intermission that somebody on the other side of the room had the very same sensation. The emcee’s attempt to duplicate this feat involves scanning each row, back to front, one end to the other, literally making eye contact with everyone in the room. It takes a full minute, at least.

“Ladies and gentlemen, boys and girls,” he declares when he’s finally through, “I am the greatest actor that has ever existed.”

Could it be true? No, it is not true. As played by the delightful Julian Bleach, the emcee is gloriously bad. He is a kind of actor/mismanager, attempting to provide thrills but mostly announcing his own fecklessness. Over the next 90 minutes, cues will be dropped, and so will wigs. The band will be urged to hurry it up already. In a desperate attempt to please, the emcee’s dance interlude will end when he tumbles to the floor, a graceless tangle of limbs.

It all makes “Shockheaded Peter” one of the funniest shows around. More than that, the emcee’s antics give the show immediacy and flair. According to the press kit, the actors may ad-lib from night to night. The whole show has a wonderfully spontaneous vibe. In the audience you feel as if you’re part of the commotion, and not just during the sing-along portion of the show. The lyrics (adapted from Hoffmann by Mr. Jacques) end so often with the same refrain that, when signaled to join in, we know to sing that another imperfect tot is “dead, dead, dead.”

The show’s odd, old-timey stagecraft also captures Hoffmann’s tone, balancing the fantastical with the didactic. The evening is framed by the story of a respectable husband and wife (Anthony Cairns and Tamzin Griffin) who want a baby, only to have a stork deliver a freaky, frazzle-haired, long nailed monster. They lock him away under the floorboards – a metaphor, maybe, for all our dark submerged tendencies. “The wise man sees the error of his way, the fool passes on and is punished,” intones the emcee more than once. For all its hilarity, some moments, like the wistful ballad “Flying Robert,” about a boy carried away by the wind, are really moving.

But the show never feels heavy-handed, never moralizes. The tempo drags here and there, but it’s too much fun to feel preachy. Mr. Crouch and Graeme Gilmour’s scenic design is one part cabinet of horrors, one part Punch-and-Judy stage. The special effects – a dress bursting into flames, a monster rampaging around – are lo-fi and extremely effective. Even the band is part of the spectacle.

Adrian Stout would look just like Max Beckmann, if the painter had been playing the double bass in his self-portrait instead of dangling a cigarette. Adrian Huge, the best-named drummer in history, bangs giddily away on what looks like a toy set and, on occasion, kitchen pots and pans. Mr. Jacques can be tough to understand at times – clarity’s tricky when you’re singing at a pitch high enough to shatter glass – but he exudes style, even in his walk. He shuffles after the emcee in tiny centipede steps. Like so much else in this show, he is neither entirely in our world nor out of it.

(422 W. 42nd Street, at Dyer Avenue, 212-239-6200).