In 1979, Ziggy and his siblings, Cedelia, Stephen and Sharon, made their recording debut with their father, "Children Playing in the Streets". The Melody Makers, as the group came to be known, played occasionally for several years, including at their father's funeral. His father, Bob, died in 1981. Their debut LP was Play the Game Right, which was a very pop-oriented album, earning Ziggy some derision from critics. The band's label, EMI, wanted to market Ziggy as a solo act, and so the Melody Makers moved to Virgin Records, where they recorded Conscious Party (1988, produced by Chris Frantz and Tina Weymouth). The album was critically and popularly successful, as was One Bright Day (1989) and Jahmeyka (1991).
As the 1990s continued, the Melody Makers' sales slowly declined, beginning with Joy and Blues (1993), Free Like We Want to Be (1995) and Fallen Is Babylon (1997). Ziggy had become politically active by this time, working with the United Nations and creating a record label called Ghetto Youth United. A solo album, Dragonfly was released on April 15, 2003.