Joseph Morpurgo's solo hour starts with scratchy old American TV footage. We see a local news bulletin about a fire in Odessa, Texas, then some naff adverts for local businesses. The rest of the show finds Morpurgo – one of the stars of improv hit Austentatious – connecting these snippets to tell the tale of a female cop charged with solving the mystery of that blaze. It's fitfully brilliant, but it's also overloaded. Morpurgo goes off on too many outlandish tangents, which showcase his freewheeling imagination but at the expense of a fleshed-out story or consistent laughs.
There's great stuff in here, though, starting with the sexist chief of police compulsively asserting his own machismo: "Sorry," he'll bark, "I can't hear you over the sound of my prostate." The next scene transports us to the office of local diamond trader Ardan, who gives us a workshop in the jewel he calls "fit gravel". In a highly energetic performance, Morpurgo keeps the audience actively involved in proceedings, up to and including a denouement that upends the stage/auditorium distinction entirely.
The least effective element of the show is its midway subplot involving a reindeer on the run from a malevolent Santa. In principle, it's an amusingly odd choice to dress up as a reindeer, and depict its lovelorn life. Or to perform in the character of static electricity – a scene which finds Morpurgo intoning a beat poem about white noise. I admire the unpredictability, but neither skit is engaging or funny enough to justify the wide detour from the story so far. When he's good, he's very good – the comically labyrinthine reveal at the end, toying with the daft conventions of whodunnit fiction, is another example. The problem with Odessa is that, quite unnecessarily, he's trying too hard to show it.
• Until 25 Aug. Box office: 0131-226 1000. Venue: Pleasance Dome, Edinburgh.