Edinburgh Festival 2013 comedy review: Just what we need - a pen of one's own

In a time of rich pickings for comics, feminists get the best laughs

Aisling Bea, pictured, and David Baddiel, both raise laughs at the Fringe (Aisling Bea)

Sometimes a comic has a moment, and Bridget Christie is having hers. I used to find her surreal comedy – when she dressed as a donkey, or an ant or some such – just a little too fey, lightweight even, but in A Bic For Her (The Stand until 25 August *****) she dares to take on the heavyweight subject of feminism.

It's a subject she's passionate about, but she's never preachy. Rather, she uses absurd arguments – taken to the point of stuttering rage – to ridicule everyday sexism, linking Sir Stirling Moss's fall down a lift shaft to his opinions about female racing drivers, or suggesting a suitable tennis-ball-based punishment for John Inverdale after his comments about the Wimbledon champion Marion Bartoli.

She also uses the sneakily clever device of putting words into hecklers' mouths to comment on the worst aspects of misogyny, and never has audience participation worked to such great effect. Her direct action on lads' mags in supermarkets, meanwhile, is inspired.

Christie is a wonderful physical comic, too, acting out to hilarious effect a scene in which the Brontë sisters realise that they can't write their masterpieces because the A Bic For Her, "in a range of pastel shades with an easy-to-hold grip" for delicate little fingers, has not yet been invented. There are some misguided fools who think that feminism can't be fun – Christie disproves that, and how.

David Baddiel (whose show ends on Sunday) last did solo stand-up 16 years ago, while he was still at the height of his fame. He's now a novelist and rather less famous; meanwhile, the cult of celebrity has grown to hideous proportions in the intervening years – so he's ideally placed to perform Fame: Not the Musical (Assembly George Square ****), a witty and intelligent examination of the corrosive effects of celebrity. "Fame distorts every aspect of your life," he says, referencing a respectful visit to Auschwitz that was interrupted by a fan's question about Fantasy Football.

By its nature the show is laden with starry names, but Baddiel drops them with aplomb and the anecdotes are highly amusing – and all at his own expense. He recounts events at a showbiz party where there was a farcical series of mistaken identities, and how he's now convinced that Lord Lloyd-Webber is under the impression that Baddiel is Ben Elton (another bearded bloke off the telly), while Madeleine Lloyd-Webber just thinks he's a rude git.

Baddiel has triumphantly risen above what, in others' hands, could be self-indulgent blah, and the hour goes by too quickly.

Ed Byrne is a nicely cynical observational comic who always produces witty and well crafted shows, and The Roaring Forties (EICC until 25 August ****) is no exception. It's about getting to an age at which he is doing a spring clean of his life, and working out that "there are seven billion people on the planet and I only have time to be friends with 10 of them". So out go people who don't indicate at roundabouts, or those who use trite phrases such as "touched a nerve there".

The energy builds steadily as Byrne talks about looking like Vicky Pryce and doing a speed awareness course (the two are unconnected), where his quick wit nearly earned him extra points. The material about his forthcoming vasectomy is particularly strong.

Another Irish comic, Aisling Bea (C'est la Bea, Gilded Balloon *****), who won last year's So You Think You're Funny competition, has a gloriously daft hour in which she guys Irish stereotypes. She has a death-obsessed mother and gives at least one extra syllable to the word "potatoes", while her interesting explanation of the famine is that Ireland is surrounded by the sea "but they couldn't eat fish without chips".

This is a very well structured hour, and there are superb riffs about Ireland's collective madness, greed and corruption during the Celtic Tiger years – "giving mortgages to 12-year-olds" – where her anger is barely masked. A hugely accomplished debut.

Edinburgh Festival Fringe to 26 Aug (edfringe.com)