Fred Schneider and Kate Pierson handle the lead vocals on this one. Their bandmate, Cindy Wilson, explained in a 2019 Songfacts interview
how it came together. "'Mesopotamia' was a cool song," she said. "It came from a poem Fred had. We were all jamming on it, so Kate and I got out licks like, 'Throw that beat in the garbage can!' That's one of my favorites now - I wasn't so crazy about it at the time, but now it's really one of my favorites."
Cindy's brother, Ricky Wilson, was the guitarist in the band and added an inventive touch to this song. Said Cindy: "Ricky's guitar, oh my God, it's so modern. It still sounds so modern to me. But Kate and I got to jam on that one and put our touch on it."