"Goodbye Girl" was the first single released from Squeeze's second album Cool for Cats. Three different versions were recorded: one for the UK single, one for the American single, and one for the album. In the UK, the single reached number 63 on the UK Singles Chart.
Notably, in live performances, the band strayed away from its gradually-paced, synth-based version in favor of a more fast-paced version featuring a heavy honky-tonk influence, similar to contemporary acts like Rockpile.
In 2007, the just-reunited Squeeze recorded a new, guitar-heavy version of "Goodbye Girl" for an Under Armour television advertisement. The Shins covered the song for Levi's Pioneer Sessions in 2010. Tarkio, featuring Colin Meloy of The Decemberists, recorded "Goodbye Girl" in 1998. It was released on the Kill Rock Stars record label in 2006.