Johnny Marr of The Smiths played guitar on this track and also on the song "(Nothing But) Flowers
." Steve Lillywhite, who produced the album along with the group, brought him in.
Marr says "Cool Water" is his favorite song on the album. He told Uncut
: "That was something David [Byrne] and I built up one afternoon. I was playing and he was encouraging me and egging me on to try different things, miking up a semi-acoustic 12-string without putting it through the amplifier and putting it into weird tunings and drones. That in itself was really invigorating."