In a world of fable, not all that different from our own, a family live in quiet harmony and feast on fruit from an exotic tree. But a storm comes; a malevolent storm, which turns neighbour against neighbour and forces them out of the land they call home. Told using puppets, this new show from Fringe regulars Box Tale Soup offers allegorical insight on the forces driving modern-day migration.

It's inspired by the real-life experiences of musicians the Stone Flowers, whose songs are an equal part of the production. In a full performance, we're told, the singers would be present on-stage; in this Fringe version we see them on a video screen, which initially I found distracting but later came to welcome as a complement to the live puppetry. The music both enhances and balances the story, sometimes sad, but often lending a hopeful tone to an otherwise grim scenario.

The live performance, meanwhile, is defined by elegance and precision. The elegance is born of economy: carefully-draped fabric is enough to evoke a mountain, while a journey is symbolised by a series of coloured throws, blue for crossing the sea and red for tramping the desert. The precision, meanwhile, is evident from start to finish. Every move is crisp and perfectly placed, delivered with a sense of ceremony, throwing all the focus on the story being told.

That story holds no great surprises, but there are striking moments all the same. The imagery of the migrant family being turned away from country after country manages to be both poignant and visceral – while a miraculous reunion in a place of safety proves less of a fairytale ending than it seems. A rapacious people-smuggler is a bewitching, fascinating fantasy creation, and proves that performer Noel Byrne is every bit as capable as a physical actor as he is as a puppeteer.

A few creative decisions didn't quite work for me. I'd have liked to have heard The Stone Flowers' stories first-hand, but strangely – even though they featured on the video – they were speaking in untranslated French. A scene set in a government office is intentionally monotonous, but went on for so long that it broke my immersion in the piece. And I was a little confused by the ending; at the time I thought one of the characters had been deported, but now, given how little fuss they made of it, I wonder if they were just putting the puppet away.

Overall though, this show is a perfectly-formed package: thought-provoking without ever preaching, a successful melding of different art-forms and cultures. There's just one more opportunity to see it at this year's Brighton Fringe. Catch it before it's gone.