The Jimmy Giuffre Trio has been played on NTS in shows including Sees to Exist Show, featured first on 24 September 2017. Songs played include Jesus Maria, Phoenix and The Chanting.

The Jimmy Giuffre 3 is any of several trios lead by Jimmy Giuffre between 1956 and 1963. The first consisted of Giuffre (primarily playing clarinet), Jim Hall on guitar, and bassist Ralph Pena (later Jim Atlas). They had a minor hit in 1957 with "The Train and the River". In 1958, Atlas was replaced by valve trombonist Bob Brookmeyer; the instrumentation for this unusual trio without a rhythm section was supposedly inspired by Claude Debussy. During 1959 and 1960, Giuffre returned to a more conventional trio (but still unconventional music!), keeping Hall on guitar and using several different bassists, including Ray Brown and Red Mitchell.

In 1961, Giuffre formed a new version of the Jimmy Giuffre 3 which played a radically new kind of music. The trio had Paul Bley on piano and Steve Swallow on bass, and while their trio was mostly overlooked at the time, they are sometimes cited as one of the most important trios in jazz history. Their collective improvisations were a kind of free jazz very different from that later played by artists such as Albert Ayler; instead, they had a quiet, intense focus with a much more melodic sound. However, their music was too far ahead of its time for most audiences. The group disbanded in 1963, reportedly after a night when the take for each musician was only 35 cents.