Richard Carpenter was Karen Carpenter’s brother. He played the piano, he composed songs, and arranged them too. But really, everyone only remembers him because of who his sister was. In Richard Carpenter is Close to You it’s 35 years on from Karen’s death, and he’s still trying to get recognition and find his own way.

We find Richard playing gigs in The Purgatorium in a parody of a Carpenters concert – treating his audience to a stream of their hits, but with none of the proper lyrics, allegedly to stay on the right side of copyright laws. It's very funny, but it also suits a portrayal of Richard trying not to listen to Karen, desperately trying to persuade everyone of his value. He was glad when Karen took over more and more of the singing, as it left him free to write songs, do the orchestrations, all the things that really made the Carpenters great; but it’s hard to be eclipsed by your kid sister.

The solitaire Carpenter performance is well-conceived. His attempt to show off as a multi-instrumentalist is fatally undermined by having to do all the switches, leaving the flute embarrassingly stuffed between his legs as he rushes back to the keyboard. Some of the rewritten lyrics are hysterical – Why Do Birds Suddenly Appear features fish instead – and when he finally sings a recognisable Carpenters medley, it’s so constrained by the “fair use” copyright limitations it takes genius to pull it off.

Matthew Floyd Jones is superb in bringing to life his own script. As a talented musician he is more than up to the task of demonstrating Richard’s virtuosity, but he also manages to convey the right amount of neediness and brittleness, in a man who wants his due credit but is temperamentally unsuited to public life.

That skill in portrayal is crucial, because this is more than just a pastiche of the Carpenters. Richard’s unhappiness and difficulty is all too real; there is a constant round of public appearances, but all anyone wants to talk about is Karen, and no-one is interested in his solo album. Despite the laughs, we end up in dark places, as he runs from the one person he misses more than anyone. When a devilish reporter tricks him into apparently diminishing Karen’s role, the controversy causes things to change. Suddenly his agent is interested in him again, but it just leads to tough questions and a final reckoning.

This is not an accurate historical representation – of course it isn't – but alongside the laughs, it’s also an extended meditation on those who live life in the shadow of someone more successful. There are entertaining mentions for Jackson siblings, David Miliband, even the brothers of Joseph (he of the technicolour dreamcoat).

So even though this is a very funny show, I’d have liked to see the darkness pushed a little further. An unlikely intervention causes a genuinely moving moment just at the end, and there is potential for even more pathos.