The original 1984 release had 11 tracks, with "Astronomy," "Tundra," "Automotive Engineering," and "General Crossing" appearing on cassette only. Now the standard release carries all 15 tracks, and the 2005 enhanced CD also contains a QuickTime video for "Lap Of Luxury".
Although it was controversial amongst Tull fans due to its 1980s electronic/synth-pop sound, guitarist Martin Barre has cited Under Wraps as his favourite Tull album. Dave Pegg, in contrast, has been quoted as saying that the tracks cut from Broadsword and the Beast would have made a better album.
This is the only Jethro Tull album where the majority of songs were co-written by band members. Usually Ian Anderson is the sole songwriter.
This is also the only Jethro Tull album that features no live drummer at all. After the recording Doane Perry joined the band on tour and became their permanent drummer.
The album was recorded in the spring of 1984 in Ian Anderson's home studio.
Songs written by Ian Anderson except where indicated.