The radio play gained by "Hats" in the US, in particular the single "The Downtown Lights", brought the Blue Nile to the attention of several well-known US-based musicians. In 1991 the band were invited to Los Angeles to work on songs by Julian Lennon, Robbie Robertson and Michael McDonald. As a result, Buchanan moved to Los Angeles and lived there for a while, and had a relationship with the actress Rosanna Arquette between 1991 and 1993. Speaking about that period of his life Buchanan said, "It really was interesting. I have to say it was lived in all earnest ... And there was much good there, I enjoyed it, I really enjoyed it ... The great thing all the time was you were constantly wanting to phone friends and say, Guess who's in the shop? Guess who's in the supermarket? I'm not immune to all that. In the movies – celluloid's better than life isn't it? It makes everything glossy. I don't mean it's better, but it's so glamorous, I met lots of people – it was fascinating." The band also worked on Annie Lennox's debut solo album "Diva", co-writing the track "The Gift". Lennox later covered "The Downtown Lights" (from "Hats") for her second album "Medusa", released in 1995.