The recording begins with the song's single-chord riff, created by a combination of Hopkins' low piano notes and Harrison's dobro, before the rhythm shifts to what author Alan Clayson calls "downbeat hootenanny" over the verses. Leng identifies the rhythm as approximating the do-si-do dance step found in square dancing. Harrison takes the first solo, midway through the track, playing a second, overdubbed dobro, while Wright's Wurlitzer electric piano leads the instrumental passage that closes the song. Contrasting with his more substantial presence on "All Things Must Pass", "Sue Me, Sue You Blues" marks a rare instance where Wright's keyboard work, rather than just Hopkins', features prominently on "Living in the Material World".