Even though the team behind Wanted: Rabbit are from the Netherlands, this short but action-packed piece of whimsy unfolded like a Dario Fo farce for three to five-year-olds.

Maybe it was the police presence with its mix of pomposity and bumbling at Chief Inspector level – the young assistant WPC is, as you might guess, as smart as paint, and therefore repeatedly over-ruled by her bumptious superiors as they try to bring a rogue rabbit to book.

There's a slapstick feel to the comic playing by the cast of three that is hugely entertaining in its own right but this Maas Theater en Dans production offsets its life-sized characters with an all-white, intricately detailed model of the town where the rabbit – a fluffy finger-puppet that pops up all over the place – is on the rampage.

At first the fierce bad bunny just munches tulips. Then carrots. But when it gnashes through the cables that carry all the communications networks it's time to say "enough" – as in "we surrender". Soon, like the bunnies, the police force is all ears and hopping madly.

It's dafter than a cupboard-full of brushes, but the execution is thrillingly exact, right down to the wee police car that "nee-naws" its way around the model in hapless pursuit of those pimpernel bunnies. We all eat carrots, afterwards.

There's more cunning sleight-of-hand and a similarly high-end attention to the tiniest of details in The Incredible Book Eating Boy (Bootworks Theatre, England). Little Henry's love of books – he eats them, literally – is revealed to audiences of one child (or lucky adult) at a time. Arrive early, in Henry's room, and while you wait to go into the special viewing booth, you'll see a harum-scarum bunch of folk – some dressed like characters out of the Oliver Jeffers's book – darting about at high-speed with little puppets or box-set models in hand.

Once you're perched inside the Black Box theatre, all that activity joins up into a five-minute saga reminiscent of a Hilaire Belloc cautionary tale. As little windows fly open and shut, like a fairground peep-show, we see Henry's taste for books become a Seriously Bad Habit. Yes, he grows uber-smart as he scarfs down tome after tome – but with no time to digest this welter of information, Henry gets muddled and physically under-nourished.

Flicka-flacka-flick. As an unseen voice tells the tale, the little windows open on framed moments delivered by an array of puppets, projections and live performers.

It passes in what feels like the blink of an eye. But the pace, the immediacy, the impact is all carefully gauged and brilliantly effective. The target audience (four to seven-year-olds) will love the feel of it being a living cartoon. Older children and adults will agree, but will probably get added pleasure from recognising the craft and panache that drives the whole show.

This year's Imaginate programme had a tremendous dance strand at its core. Belgium's Compagnie Chaliwate reflected that with Ilo, a mime and movement two-hander (for the five and over age group) that was as much about sharing and caring as it was about nurturing nature.

With few props beyond their own bendy bodies, two performers – one male, one female – created a bitter-sweet, wordless narrative about plant life in a desert where water is scarce. The tussle for survival gets acrobatically combative, hilariously so – but it shades into more melancholy territory, even if the final sad tears do cause the desert to bloom. It's rather sad to see Imaginate shut up shop at all its Edinburgh venues – dry those tears, plans are already in hand for 2014.

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