Run your eye down the columns of children’s shows in the Edinburgh Festival Fringe programme and the weasel words leap out at you: “For children and the young at heart”, “For children from six to 96”, “For children and unaccompanied adults” and a dozen more like them.

They generally mean one thing, that the companies are not really interested in children’s theatre as an art form, so they throw in a few jokes for the mums and dads, even though it alienates the children. It is a sign of how deep the disregard for children runs in our culture.

Even my best ticket to a children’s show this year, for The White Slipper, by Angel Sharp of Oxford University, claims in a generally misleading programme entry to be “for adults and children”. I suppose the “for adults” reference was to the few trifles interpolated from the adult world, such as the cowboy builders’ buzzwords, but these were aberrations in an hour of detailed and stylish drama that was good enough for anyone.

It should be axiomatic that if theatre is good enough for children, it is good enough for their parents.

The story is of a king who promised his daughter to the first man who cured his injured foot. As in all good children’s drama, the story is always being told and Angel Sharp has the theatrical inventiveness to devise ever more intriguing ways of carrying the action forward. This and the company’s sense of tempo and the delicacy with which the actors lightly toss the focus around the stage makes for engaging storytelling.

It helps that the king is tall and twice as long when he lies down. And the bedspread that covers his extended legs at other times convincingly portrays the wind, the desert and the sea. The audience was reminded again that good art can compel an adult to watch Snow White or a child Hamlet.

Good art had very little to do with The Adventures of Baron Von Munchausen.

This cheerful romp was brought to the festival by Squirrel Snatchers direct from its success in Reed’s School in Surrey and very possibly on its way to a gay and lesbian festival somewhere. The school drama club is in great form with a production redolent of the Fifth Remove in the end-of-term concert, the writers being two 16-year-olds with a talent for the sort of comedy beloved of The Goon Show, young in years but wise enough to write in parts for themselves.

The baron rollicks through the show like a young Stephen Fry, and his antagonist, whether he is a moon warrior, in ancient Rome or on the pirate ship, relishes the subversion with such glee that it seems only a matter of brief time before the pair of them are back on the Fringe in more obviously adult fare. No one upstaged them, not even the Queen of the Babies, seven-month-old Tjalline van Holk, who steals her scene by listening when she is being spoken to, and by acknowledging her applause with a beaming smile. No, it wasn’t wind.

The secret of her success is two-fold: her genes - her mother is in the business and her sister is in the cast - and a satisfied stomach, in that she had her feed an hour before curtain-up. This has been the downfall of many of her elders in her profession.

Director Ben Jeffreys takes credit for reining in all this youthful exuberance for disciplined performance and the cast deserve their ticket to the huge educational experience of being on the Fringe.

None appreciates this more, or pays more for the privilege, than the thousands of students who compete for a place in the American High School Theatre Festival at Edinburgh. I saw the Gilmour High students sift some of Aesop’s fables through contemporary American culture, psychobabble and interpersonal relationships. The clue to their enviable composure may lie in their programme biographies, which can run to a dozen lines of experience on stage, in speech leagues, forensic leagues and oratorical competition. More of them next week.

One of the great changes in the Fringe over recent years has been the influx of stand-up comedy, now grown so huge that it is being touted as a separate festival. This year it is again elbowing its way into the children’s section and very successfully, as the queues for James Campbell in the Assembly Rooms testify.

Despite having a cold, he still found enough voice to rant cheerfully about names, pets, relatives and nits for most of an hour, too long for children but you can’t take the money for less. He gets hung up on words and the odd things we always say to one another and the children laughed their socks off. Part of me laughed with them; part of me hoped the children’s fringe would not also become a scramble for television contracts.

Finally, if you bought a ticket for a turkey, I know how you feel. I went to see Four Musicians at St Augustine’s and was the only person in the audience until the company persuaded the minister and his three sons to make up the congregation. We were treated to two nursery rhymes, told not to us but to a “presenter”, in crude puppetry and incompetent black theatre to the accompaniment of an electrical storm from the microphone. The stories were robbed of their significance by the kind of political correctness that pretends to children that they live in a world without fear, dislike or death.

I’ll put it down to experience.

www.edfringe.comTickets, tel 0131 226 0000The White Slipper, August 15-16, 18-23 James Campbell’s Comedy 4 Kids, until August 25