In the early days of his BBC2 programme, The Friday Night Armistice, accusations of smugness were levelled at him. But in his new live show, called Out of His Box, Iannucci appears to be more relaxed, as though he were just chatting to a few mates - with the odd rogue heckler thrown in, of course.
Taking questions from the audience and reading extracts from his book, Facts and Fancies, Iannucci claims not to be your average "set-up/punchline" stand-up.
"I don't do jokes, as such," he announced early on at the Junction in Cambridge last Wednesday. "You know, things like: `How does a kangaroo change a tap?' `It can't. At best it can locate the source of a water- leak by jumping up and down on your house.'"
He goes on to rail against the ubiquity of stand-ups. "They do everything. You see them reading the news and doing carpentry. `Harry the Hammer Peters, stand-up carpenter - with a smile and jest, I'll make you a chest.'"
As quick on his feet as Fred Astaire, Iannucci simply dances round potential trouble-makers in the audience. When someone at last week's show shouted out, for no discernible reason, ``You're a biscuit'', Iannucci came back immediately with: ``Crumbs." He says: "That's a little response I've perfected. Only had to use it once before - when I was doing a conference for Bourbon.''
Some of the material is of dubious taste - suffice it to say that Frank Sinatra, Princess Diana, Woody Allen and George Michael all make appearances. And at close on three hours, the show could do with a bit of editing.
These are minor quibbles, however, about a performer whose surreal imagination sets him apart. For example, he constructs a compelling routine around the idea of a small village in Turkey which holds an annual Robin Cook Festival. "They sing nursery rhymes about having an ethical foreign policy and bake cakes in the shape of a hypocrite."
Later, he imagines the runners-up in a competition to choose new names for the stars of Gladiators - "Hosepipe Ban", "Antwerp", "John Pilger", and "Captain Mainwaring". And he reflects on installing a new shower-unit which promises ``three exciting water-patterns'' - ``It would be exciting if the water arched in the shape of Allah's face.''
Channel 4's chief executive was spotted in the audience at last Wednesday's show. So, what can we expect to see next from Iannucci? Will he turn up as presenter of Channel 4 News?
I wouldn't put it past him.
Armando Iannucci performs `Out of His Box' at: 28 May, The Gantry, Southampton, (01703 229 319); 29 May, The Phoenix Arts Centre, Leicester, (0116 225 4854); 30 and 31 May, the Kilkenny Festival, Ireland (056 63837).