(Andrew Maxwell)

(Pappy's Fun Club and Ivan Brackenbury)

The 62nd Edinburgh Fringe opened for business yesterday, shrouded in capricious weather and the ongoing brouhaha about the so-called Edinburgh Comedy Festival. It's hard to know whether, after another three weeks of sweating through shows in 100-seat saunas, anyone will still have the energy to worry about the name with which the Fringe's four biggest comedy venues have chosen to market themselves. But what is clear, after seeing three of last year's if.comedy award runners-up strut their stuff, is that the comedian to beat this year is Andrew Maxwell.

If Edinburgh can offer another hour of stand-up this poised, this thoughtful, this consistently caustic, I want to see it, and I want to see it now. On the surface, it's much the same as the Irish comic's past few shows: perched on a stool, he rubs up again men more desperate than himself in a trio of travel stories. But his storytelling is at a new level. Playing at a maximum security prison in Dublin, he wins his tough crowd round by turning on the screws, which prompts a sigh of surprise: “The sound of a hedgehog being brought into a primary school.” Telling us about his pair of gigs in Belfast - one for the loyalists, another for Sinn Féin - he has a socio-political nous that is sensitive yet rambunctious. Nice trick if you can do it.

In earlier shows Maxwell sometimes reined himself in with a cloyingly deliberate manner, as if to reassure us that something substantial was going on here. No longer: this is a passionate, playful comic who controls his material and his crowd with a chortling ease that belies the precision of his lines. Maxwell is a comedian at one with himself, loud but not a loudmouth; smart but not smart-arsed. The night I saw him, he faced down some heinous hecklers and annihilated them with a smile on his face. He is fiercely funny and utterly invigorating.

Of the other nominees, Pappy's Fun Club is a four-man sketch outfit whose loose, just-mucking-about manner conceals a sure sense of structure. Even so, they need big set-pieces to keep them the right side of jolly amateurism, and the first half of their show Funergy lacks the calibre of last year's Bob Dylan routine to help to shut down all critical faculties. Thankfully, their outsized ideas - warring stuntmen, an evil whale, casual racism, the greening of the Fun Club - all come together in a second half full of backbiting, inspiring homemade props and silly songs. Patchy, but very, very likeable.

Ivan Brackenbury's Hospital Radio Roadshow was the funniest show of last year - but its Christmassy follow-up, perhaps inevitably, is not as fresh. Tom Binns, who plays the Chesterfield DJ, has done well to raise the stakes - a hospital manager threatens to shut Ivan down if he can't stop causing offence - while continuing to play inappropriate songs for stricken listeners. As Ivan shuffles behind his decks, playing Great Balls of Fire for a man with a botched vasectomy, that joke still works. If you've not seen Ivan before, go, enjoy. If you have, you'll have fun, but it's a sequel: the element of surprise has gone.

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