Hard-hitting theatre is all very well, but sometimes you just want a rollicking comedy caper. Thank the Fringe gods, therefore, for Defective Inspector, a slick and buoyant parody of the crime-thriller genre – and of many other things besides. A hilarious tale of dogged police-work and political intrigue, it features snappy one-liners, implausible plot twists and a rather well-executed umbrella fight.

At the centre of it all stands the Defective Inspector himself, narrating the tale with jaunty eyebrows and a sardonically-upturned mouth. Played by Harrison Cole, who also wrote the script, he’s a perfectly-tuned comic creation: suave, self-assured and the hero of his own tale, yet unable quite to hide the buffoonery below the veneer. He has a particular talent for choosing exactly the wrong word for what he wants to say, and the Englishman-abroad schtick is gleefully exploited, though never overplayed.

Though Cole’s a near-constant presence on stage, he’s surrounded by a spinning whirligig of additional characters with oh-so-familiar roles and conveniently-punnable names. There’s the hard-boiled police chief, the corrupt mayor, the mysterious assassin… all played with verve by Ellie Church, Francesca Eldred and Daniel Hemsley. But the best character of all might be a dog – the adorable (or is he?) Mr Fluffington. In an inspired recurring joke, Hemsley both cradles a cute plush toy and acts out its enthusiastic yelps, in the process becoming a fully-realised human puppy.

There’s a second layer to the comedy, as we’re told at the start that the money ran out and we’re seeing a troupe of amateur actors taking the stage. Make no mistake though, the ensuing bumbling is strictly for giggles; in reality this production is tightly-choreographed, slickly-performed, and all the funnier for being played with a completely straight bat. Blatant innuendo is uttered with childish innocence, while the cast’s “mistakes” are marked with a sharp look and nothing more. There’s just enough acknowledgement of the audience to bind us in, but not so much as to break the spell.

If there’s a criticism to make, it’s that it lands very lightly – once it’s over, it’s hard to remember quite what happened or exactly why you laughed so hard. For the time you’re in the theatre, though, this is a truly joyous show, the kind that you just feel better for going to see. If you’re planning your own Fringe odyssey, schedule a stopover here.

And there’s more: While Defective Inspector: American Odyssey stands perfectly well on its own, it’s paired at the Fringe with its sequel Defective Inspector: A Stitch In Time, with the two episodes performing on alternating days. A Stitch In Time is a newer work, and it occasionally shows – it doesn’t yet have the perfectly-nailed cohesion of the much-better-travelled American Odyssey. But it still earns 4* for an impressively-convoluted time-travelling plot, a bravura comic interpretation of a bit-part historical figure, and a gloriously extended multi-scene joke involving a pair of handcuffs (which ends with, quite genuinely, the funniest pay-off I can remember seeing at the Fringe). If you can only manage one, make it American Odyssey… but see them both if you can.