The name of the label was a pun derived from disc and the Compatible Discrete 4 process of encoding quadraphonic sound signals into phonograph records.
Another notable act on the label was Ted Nugent and the Amboy Dukes, who recorded their final two albums for DiscReet.
Among their arguments was that Cohen had signed record deals with Kathy Dalton and Growl, two acts which Zappa did not approve.
The later three of these disputed titles had no songwriting or production credits and used cover artwork by cartoonist Gary Panter, which was not approved by Zappa.
In 1988 and 1989, DiscReet recordings by Tim Buckley and Ted Nugent and the Amboy Dukes were briefly re-issued on CD and cassette by the Enigma Retro label.