Melody Maker described the song as "a brightly unexpected mixture of black steel and pop disturbance" and qualified its genre as "thirties hip hop".

They then said : "If this nation was served by anything approaching a decent pop radio station, "Peek A Boo" would be a huge hit.

The song was built on a loop in reverse of a brass part with drums which the group previously arranged a year before for a cover of John Cale's "Gun".

[7] The band selected different parts of that tape when played backwards, editing them and re-recording on top of it, adding a different melody plus accordion, a one-note bass and jarring guitar.

When initially composed to be an extra track for 1987's "The Passenger" single, the band realized that the song was too good to be relegated to B-side status and deserved better exposure.

[12] A minor controversy ensued after the single's release, as the lines to the chorus ("...Golly jeepers/Where'd you get those weepers?/Peepshow, creepshow/Where did you get those eyes?...")

To remedy the situation and to avoid legal action, the band gave co-songwriting credit on "Peek-a-Boo" to Harry Warren and Johnny Mercer.