Edinburgh Fringe: Jigsy/Pappy's/Joe Lycett

Jigsy, Assembly Rooms ****

Les Dennis may have started his career as a comic, and then as a presenter of cheesy, family-friendly television game shows, but of late he has been plying his trade as a very decent actor. And so it proves again in Tony Staveacre's one-man play about a washed up Liverpudlian club comic.

It's set in 1997 in a Liverpool working men's club, a beast that has mostly rolled over and died these days. Jigsy, florid of face and never seen on stage without a pint in his hand, does his two spots either side of the bingo. He has worked with some of the greats - Ken Dodd, Peter Cook, Tommy Cooper and, er, Cannon and Ball - and there are some cracking anecdotes about them; Cooper and Cook's legendary drinking, Dodd's legendary meanness. I'm not quite sure how the Dodd material got past a lawyer, but it's funny none the less, and Jigsy's reminiscences about the old days strike me - as someone who has spent rather too much time hanging around comics, both old-school and new wave - as entirely believable.

If the insider tales about the comedy industry are the light, the shade is provided by a story about a funnyman whose personal life has been a disaster, but who became hooked on the applause and the freedom a life on the road afforded him to piss his life away - in more ways than one. In one of the many affecting moments of the play, Jigsy recalls one of his three children, whom he rarely saw, as saying, “I think I know what it's like to be an orphan.”

Dennis gives a beautifully nuanced performance in a play that combines a deep love of the comedy industry with a clear-eyed awareness of its pitfalls.

•  Jigsy is at Assembly Rooms until 26 August

Pappy's: Last Show Ever! Pleasance Dome *****

Pappy's started life as Pappy's Fun Club with four members – Ben Clark, Matthew Crosby, Tom Parry and Brendan Dodds. They won an Edinburgh Comedy Award nomination in 2007, and then after Dodds left for other projects, the remaining three morphed in Pappy's. Their shows have a distinctive madcap mix of sketch, physical comedy and songs, and it's all good fun, but my bugbear in the past has been their constant corpsing, much of which appeared scripted. But in Last Show Ever!, Pappy's have crafted a very fine piece of entertainment, packed with jokes and performed with elan.

The show is neatly framed by the device of having them, as old men, looking back on why this was their last show. This is dangerously close to sentimental, but they just about pull it off, because what is performed in between is so joyously funny and inventive. They pack in visual jokes, puns, music gags and all-round silliness, referencing vampire priests, daft gameshows, the Wizard of Oz (a brilliant running gag) and, er, gloves.

My favourite section is a beginning-to-end love story performed (with the help of a woman from the audience) to Billy Joel's "She's Always a Woman". It's an inspired joke but they then top it with a throwaway line after the sketch is over. Huge fun.

• Pappy's are at Pleasance Dome until 27 August

Joe Lycett: Some Lycett Hot, Pleasance Courtyard ****

There aren't many comics who announces they are bisexual almost in the first sentence of their show, but newcomer Joe Lycett does, and then goes on to tell us why he doesn't like his penis. But this isn't crude comedy, and actually his set would barely shock your proverbial maiden aunt - apart from the occasional cock joke and a hymn to the joys of Grindr, that is. Otherwise it's about working out what “being a man” really is - is it the football-loving homophobic bullies at his school, his girl-obsessed personal trainer - who says things like “I can lift a car” without prompting - or Jim Davidson, with whom he once worked?

There are times when Lycett appears to be channelling the spirit of Julian Clary, but that's all to the good. He's a very personable comic with a nice line in irony and self-deprecation who knows how to work an audience and charm those who perhaps don't share his social, er, interests (there was a precious moment in the show I saw where Lycett had to explain what Grindr was to a middle-aged Celtic fan). This show is his full debut at the Fringe, and I suspect we'll be seeing a lot more of him.

• Joe Lycett is at Pleasance Courtyard until 26 August