1982 - Garlands (320 Kbps) 1983 - Head Over Heels (320 Kbps) 1984 - Treasure (320 Kbps) 1985 - The Pink Opaque (320 Kbps) 1986 - Victorialand (320 Kbps) 1988 - Blue Bell Knoll (320 Kbps) 1990 - Heaven Or Las Vegas (320 Kbps) 1991 - Cocteau Twins Singles Collection 10CD (320 Kbps) 1993 - Four-Calendar Café (320 Kbps) 1996 - Milk & Kisses (320 Kbps) 1999 - BBC Sessions (2CD) (320 Kbps) 2000 - Dark Treasures - A Gothic Tribute To The Cocteau Twins (Cleopatra Records) (320 Kbps) 2000 - Stars And Topsoil A Collection (1982-1990) (320 Kbps) 2001 - Eyes Are Mosaics (192 Kbps) 2001 - Twin Eyes (Rarities) (VBR Mp3) 2005 - Lullabies to Violaine (4CD) (320 Kbps) 2018 - Treasure Hiding The Fontana Years (4CD) (320 Kbps)
Fraser was the vocalist and lyricist in Cocteau Twins, a group founded in 1981 by Robin Guthrie and Will Heggie. At the time, she was only 17 years old, and had never thought of herself as a singer. Guthrie and Heggie noticed her dancing at a club one night, and asked her to join their band. After an on-off phase, the band recorded some tracks which were sent as demos to John Peel and Ivo Watts-Russell of 4AD which led to their being signed by the London-based label and a successful career in music. Fraser and Guthrie formed an intimate relationship, the couple having a daughter, Lucy Belle, in 1989. Guthrie liberally used drugs and alcohol through the years, and Fraser suffered a nervous breakdown during the recording of Four-Calendar Cafe. Following the long string of turbulence the couple broke up in 1992, still opting to continue a musical relationship until 1998, when Cocteau Twins were finally disbanded.
Fraser also had an intense personal relationship with singer Jeff Buckley and recorded a duet with him, "All Flowers In Time Bend Towards The Sun", written by Buckley but never released commercially. She speaks candidly about their relationship in the BBC documentary, Jeff Buckley: Everybody Here Wants You.
Cocteau Twins were due to perform for the North American Coachella Festival on 30 April 2005. However, a statement issued 16 March 2005 by the band's management said: "It is with regret that Cocteau Twins announce they will not be performing at the Coachella Valley Music & Arts Festival as had been planned. Due to personal reasons, member Elizabeth Fraser has decided that she is unable to participate in the reunion, and apologies for any inconvenience this has caused. No future plans for any reunion are currently being made. Our sincere thanks and apologies to all the fans and media who wrote to us expressing your enthusiasm and support."
During the years of working as part of Cocteau Twins, Fraser also collaborated with numerous artists, appearing on 4AD house band This Mortal Coil's first release along with her bandmates where her notable contributions included a cover version of Tim Buckley's Song to the Siren, and providing one-off vocals for acts such as Felt (Primitive Painters), Dif Juz (Extractions LP), the Future Sound of London (Lifeforms EP), the Wolfgang Press, Ian McCulloch and others.