1985: Glad I'm Not a Kennedy from the album Genre, re-released on the album South in 1987.
She wasn't intending to leave London but when Laing came back to New Zealand in 1983, she ended up staying, and found herself somewhat starting over in a country which hadn't heard much from her in the past decade.
"I was just supposed to come back for six weeks because my dad had had a triple bypass. But I got used to being back in New Zealand - you know, the open skies - and thought I'd stay. It was the first time in a while that I felt I really had a goal, too - to have a hit, in the world, from here. And Glad I'm Not a Kennedy kind of did that eventually."
It was one of those songs that just arrived, almost fully formed, quite simply off the back of a TV appearance by Edward Kennedy.
"He was standing in the presidential race and that was the first time I'd seen him, and he just looked so puffed up and horrible, and I actually just said those words out loud: 'God, glad I'm not a Kennedy.' And bells went off, whistles rang and I went straight out to the shed to write it, and it was done and dusted in half an hour. It poured out."
It was a sentiment that summed up a few different ideas which had been bubbling away in Laing's head since her return to New Zealand.
"I think it also says 'glad I'm not American' in some ways, and I definitely felt like that because when I went to England in 1975 there was one KFC in Wellington, and when I came back the place was like an American colony. We'd gone from being more British than the British to this invasion of American culture. It shocked me."
Kennedy was going to be the second single from her new album Genre, which was recorded with Bruce Lynch for Pagan Records, and saw Laing exploring the world of synth sounds she'd discovered with Manfred Mann. But she found herself being somewhat ignored by radio.
"In the end, Kennedy had to chart in Australia before anyone here opened their eyes, or ears."
The fact it became popular across the Ditch also provided impetus for the song to be remixed by Peter Wilson in England and re-released as part of her next album South, in 1987.
"At the time I was upset about it. But when it came back I could hear what Peter had done, and it was an education. I could totally see or hear what was making it bounce a bit more, what was making it better."
Kennedy eventually made it to No2 on the NZ Singles Chart, and its presence on South gave that album legs, too - it ended up being released in Australia, Sweden, and the United States. Then a remix of her new single Soviet Snow made it to No18 on the US dance charts.
"That was so funny: Shona the dance queen. It was a great mix though, incredible mix."
Those two singles also sent Laing on her first tour of the US, an experience she remembers vividly.
"We went straight into New York and we stayed at the penthouse at the Marriott, the one that was part of the World Trade Centre. That's quite a hairy memory. And from there on in it was madness, six weeks across America through summer. It was great, but it's surprising any of us made it back. Dave McArtney was on that tour and he was an absolute rock, because he'd been there before. He was amazing."