At Last, the Edinburgh Fringe is under way, and we don't have to read any more of the trend-spotting articles which preceded it. One of these stated that there were 15 per cent fewer comedy shows on than there were last year, but if the posters that wallpaper the city's pubs are any indication, reports of a comedy drought have been exaggerated. There's no need for the UN to helicopter any emergency stand-ups in from London just yet.

The statistics may have been distorted by the number of shows featuring Lee and Herring, starting with their own lunchtime chat show This Morning With Richard, Not Judy. The promotional poster proves disappointingly deceptive as at no point does Stewart Lee wear a dress. For that matter, This Morning is barely a chat show at all, and it sags only when the Fist of Funsters half-heartedly invite a guest - usually a passing comic - to interrupt their own barely scripted tomfoolery.

It's more of a meta-show. Lee and Herring detail where all the ticket money goes and then they hand half of it back; they crown a "King or Queen of the Show", and they have a "Humiliate the Media Scum" segment. There's a low-gear, 12.30-in-the-afternoon feel to proceedings, which doesn't stop them being the perfect way to ease yourself into a day's comedy - especially as the "ticket auction" makes it possible to get in for 50p. Journalists should be warned that the contents of their notepads may be read out, so they should make sure they write, "Richard Herring should really do up one or two more of his shirt buttons" in block capitals.

It would be a defiant gesture but a futile one, as Herring spends one scene of his new play, Excavating Rita, rampaging naked. That aside, Rita is a delightful show, a semi-autobiographical rites-of-passage comedy about an 18-year-old boy, so naive that he thinks his college scarf is the apex of style, who joins an archaeological dig before going to university. The ensemble cast is faultless, the script well constructed, and Herring has many wise words to say about growing up, life, death, and all that sort of thing.

Lee, meanwhile, has his own stand-up hour, and it's another of those darn deconstructionist meta-shows. Much of his routine is about how he came up with his routine (he was watching late night TV at the time: "I knew it was really late because there were programmes on with Tony Slattery in them"), and it's all spiked with bored, lip-curling sarcasm. It's a bit like watching Woody Allen's Stardust Memories, and wondering whether something becomes less pretentiously post-modern if it keeps going on about how pretentiously post-modern it is - and more funny if it goes on about how unfunny it is.

There is a definite trend for drawing attention to your act's shortcomings this year, and for trying to wring a laugh out of a limp gag by appending it with "No, that wasn't a joke, it was just something I thought I'd mention". Two of the worst culprits are Boothby Graffoe and Dylan Moran, both affable, talented ramblers, and both of whom could benefit from not trying to stretch half an hour of not-all-new jokes into an hour long slot.

Graffoe - anecdotal, dopey, permanently startled by life - gives the impression that his entire act is an informal warm-up for a proper show he's going to begin after we've left. Moran - unaccountably morose for someone who won last year's Perrier Award - is best described as Eddie Izzard with a hangover. He mumbles, trails off, and loses his way; then he turns a corner and arrives at an oasis of surrealism and wit: a bachelor's cookery is "a fist of bread dipped into anything runnier than bread".

More eager to please is the up and coming Adam Bloom, a hyperactive daydreamer who is young enough to be startled by the sight of a friend of his mum's in the audience, but quick enough to turn this potential embarrassment into the funniest part of his show.

If all this unstructured stand-up leaves you thirsty for something more disciplined, seek out The League of Gentlemen, three tuxedoed dudes who take the creaky sketch formats of old (a man walks into a shop and is humiliated) and customise them into something darker and more disturbing. Not that a horrific death or a sexual deviation every five minutes is enough to carry a whole show, of course. The League build on these solid foundations with extreme cleverness, exceptional acting and original characters, (a particular favourite is the troubled cave-guide). They're as funny as they are sick, which is saying something.

Speaking of leagues, Simon Munnery plays the League Against Tedium in his show, Cluub Zarathustra. Cluub Z, as it's known, was recommended to me as a radical new concept in a Dadaist anti-comedy, but mercifully it's nothing of the sort: it's quite amusing, instead. Munnery has replaced Alan Parker, Urban Warrior, with a new egotistical inadequate character - this time a snivelling megalomaniac - and given him a new brand of aphoristic one-liners. Oh, and Stewart Lee crops up in this show too.

This week's king of comedy is Al Murray as the pub landlord in King Of Beers. Murray is currently best known for exclaiming "No, you go first," on Channel 4's Harry Hill Show, but will soon be famous for this bigoted rotweiler, this outrageous bar steward, this third Mitchell brother, the one the other two don't like to talk about.

The landlord treats us to a polished rant about time, the French, why the serving of spaghetti in pubs is tantamount to high treason, and the secrets of evolution: we're separated from the animals by "beer - and reason, obviously". He is a completely realised character: a monster, but also a man who is almost loveable as he cries the praises of lager and of his son, Carl (short for Carlsberg), and almost tragic as he struggles - veins popping out of his shaven head - to twist the unruly, unkind world into the neat shape it is in his dreams. Mostly, though, he's just fantastically funny.

All shows at the Pleasance (0131 556 6550), until 30 Aug