The Fringe can be make or break for the ambitious circuit comedian and it looks like it is about to make Shappi Khorsandi. After a few years of treading water, Asylum Speaker draws heavily on her family history and is easily her strongest show yet.

Khorsandi certainly has some interesting source material. When she was small her family was forced to flee from Iran. The Ayatollah had come to power and her satirist father, Hadi, became an enemy of the state.

Even in Ealing, Hadi's life was in danger and for a while the Khorsandis had to go into hiding. Shappi's private way of deadening the fear was to become bulimic.

This might not sound like comedy gold but confident delivery and lightness of touch uncovers the funny side of a dark period. The narrative is usefully propelled by simple, crowd-pleasing gags.

As a child she recalls how she had to put up with English schoolfriends nicknaming her Shakatak. Modern Iran should have "a more moderate leader, a mullah-lite".

In the right hands, Fringe shows dealing with personal issues can pack a powerful punch. Dara O'Briain once delivered a great set inspired by his late grandmother's IRA past, while Adam Hills broke through with a poignant piece about his prosthetic foot.

Khorsandi's tale of safe houses, Dickensian poverty and racism is up there with the best. Do not be fooled by the Blue Peter smiles.