Edinburgh 2013: Tig Notaro/Joe Lycett

Tig Notaro, Gilded Balloon ****

“I've been busy. I've been growing my hair out.” Not the the most animated start to an hour of comedy, but that's how American Tig Notaro begins Boyish-Girl Interrupted, one of the most original 60 minutes I've seen at the Fringe, and certainly the most laidback.

Those who are familiar with her personal story – she underwent a double mastectomy last year, spoke about it at the Largo comedy club in Los Angeles and it went viral after Louis C.K. tweeted about it – might have expected the growing-her-hair-out thing to be chemotherapy-related. But no, she's just shooting the breeze with the audience, one of many sections where she spins out seemingly a tiny bit of material to a substantial part of the show.

Notaro does talk about the cancer, albeit briefly, and wonders whether it was her breasts ganging up on her after years of her making jokes about them being small - “You know what, we're sick of this. Let's kill her” - which is possibly the darkest yet funniest joke I've ever heard about breast cancer.

But mostly she just riffs - about the strange spelling of diarrhoea (and don't get her started on the US version), weird swimming pool signs and her “friendship” with 1980s singer Taylor Dayne - and builds up a wonderfully surreal picture of her audience; people sitting at the side of the stage are a show waiting to come on and people eating crisps in the balcony are conspiring to throw her off her act, while anyone with a distinctive laugh is questioned, and she mines some comedy gold from these exchanges.

Even when she is firing down volleys at hecklers and latecomers Notaro undercuts her stern looks by saying “only joking!” and her warmth always shines through as she is in absolute control of the house. This is a memorable UK debut from a most individual comic.

• Until 26 August

Joe Lycett, Pleasance Courtyard ****

Joe Lycett made an accomplished Fringe debut last year and If Joe Lycett Then You Should've Put a Ring On It is another pleasing and undemanding hour of comedy. That's not to slight him, as Lycett has no pretence of writing a show with a grand theme or even a narrative arc; this is mostly just him chatting to the audience about his life (or a version of it), and it works.

He starts with a football gag - “One more than you were expecting” - a neatly oblique reference to his camp persona, and does a lot of audience interaction. He's a generous host and even when someone slightly out there joins him on stage to take part in his game show (“gay or not gay?” - everything from lavender oil to kumquats) and she won't shut up, he silences her with catty but not cruel put-downs.

The material, about sending annoying complaint letters to companies, branding food - “you can't be angry buying cheese puffs” - and having a naughty alter ego, is hardly substantial, but Lycett is an immensely likeable presence on stage. Expect him to be hosting that show, or something very much like it, on television soon.

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