Biography
The Bleeding Heart Band was the name gave his backing band for a brief period of his post-Pink Floyd solo career.
Although Waters released "The Pros And Cons Of Hitch Hiking" in 1984, and toured as a solo artist promoting that album (with an unnamed supporting band), he was still technically a member of Pink Floyd, and did not officially leave the group until late 1985.
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His first album as an ex-member of Pink Floyd was the soundtrack to "When The Wind Blows" in 1986. It was for this soundtrack album that the band moniker "The Bleeding Heart Band" first appeared.
Biography text from Last.fm, available under CC BY-SA.