His style is what you might call "Irish Rover". You never quite know where an anecdote is going to lead, but that's a major part of his charm. As with Billy Connolly or Eddie Izzard, it's the getting there rather than the arriving that matters with Jimeoin. "Sometimes I can't think what to talk about," he cheerfully confesses, before cracking one of his winning, "cheeky chappie," toothless smiles (he claims his teeth are "too wee" to be seen without adopting the most unnatural-looking rictus).
In an era when it's trendy to appear on stage as a security guard or a Page Three girl, Jimeoin is almost passe in just being himself during his set. Without once having to resort to the dressing-up box, he tells warm, personal stories about avoiding his mother's remonstrations and his father's right hooks. He recounts that his sister gabbles on the phone so much that "even if she gets a dirty phone call, the guy's going, 'Look I really must be going now' ".
Much of the act at the Cochrane Theatre revolves around a good old-fashioned search for the mythical common ground. "As a child in the car," he asks, "did you ever get home late at night and pretend you were asleep, so you didn't have to carry anything in?"
But homeliness is not next to blandness. Jimeoin can let his imagination run riot with the best of them. He wonders, for instance, about that calm period in the middle of a washing-machine's cycle: "I always expect to pick the lid up at that point and catch it having a cigarette and a beer." He goes on to do impersonations of bits of fluff and "that hard tissue you get in your pocket" after washing. As he comes on stage for the second half, he happens upon the junction-box for the microphone: "Here's a black box," he quips, "just in case we all crash."
Later, he whips out a guitar and sings a hymn to the rubbish everyone accumulates in "The Third Drawer Down": "one chopstick and ashtrays from New Zealand / things you think will come in handy, they just never do".
All comedians are desperate to be loved - and, judging by the whooping reception, Jimeoin certainly is. A Jimeoin concert is one form of craic you can take without damaging your health.
n Cochrane Theatre, London WC1 (0171-242 7040) to 3 Aug, and at the George Sq Theatre, Edinburgh (0131-226 5138) from 11 to 26 Aug