The album balances traditional song structures on the "left side" with more free-form improvisation on the "right side", fitting somewhere between the experimental Discipline and the more commercially accessible Beat. Tony Levin had more input than on any other King Crimson album. The "other side" on the 2001 remaster consists of bonus tracks including an a cappella in which all four members supposedly sing in a barbershop quartet but is really Levin's voice overdubbed to create harmonization.
The name of the album is based on the idea of perfect opposites and "three sides to every story", or his, hers, and an objective truth.
Tracks 10-15 were added for the 2001 30th Anniversary remaster. Two of the three "Sleepless" mixes were previously available on the UK 12" single. The Bob Clearmountain mix appeared (incorrectly credited and against the band's wishes) on the U.S. Warner Bros. LP pressing.
Released on 27 March 1984, Three of a Perfect Pair reached number 30 in the UK Albums Chart
Trouser Press described it as "a most disjunct album from a band that prided itself on carefully matched contradictions. The Left Side sports four of Adrian Belew's poorer songs and a self-derivative instrumental; the flip is nearly all-instrumental, nearly free-form, nearly brilliant. [...] Apparently the Frippressive "discipline" that forged the critically acclaimed pop/art synthesis of the first two latter-day Crimson albums is not a permanent condition."
During an interview on BBC Radio 1 in 1984, Robert Fripp described the album's 'left' side as "accessible" and 'right' side as "excessive".
A new 5.1 surround sound mix by Steven Wilson and Robert Fripp was released in October 2016 for the 40th Anniversary Series as a standalone CD/DVD package and as part of the On (and off) The Road 1981 - 1984 boxed set.