Fun was originally planned as the first single from Carmen Electra's first album, then titled On Top (with the artist credit "Carmen") in 1991, and promotional copies were pressed (with the artist credit "Carmen"), but the single was left unreleased when the album was postponed; the pressed promotional copies of the single were released through the 1-800 New Funk phone service in 1998, however, on both 12" vinyl and on cassette.
Although the single was on the label Paisley Park Records, that record label had closed over four years earlier.
The single contains an extended version of the track Fun, as well as Mo' Fun, which is essentially the extended portion only. Fun featured Prince as a co-writer, producer and performer.
Receiving only a limited release, the single was not eligible for the charts.
Interestingly, the single's artwork contains only the word "Shhh!", meant to elicit intrigue, since the single was intended as a promo single for DJs (similar artwork was used on a promo single of the album's eventual first single Go Go Dancer). The track Shhh, recorded in June 1992, is unrelated to its use here.