Upon leaving the Cure, Dempsey became the bassist for Scottish band the Associates, who (like the Cure) were signed to Fiction Records. He had already performed with the Associates prior to leaving the Cure, but made his debut as their new full-time bassist on 16 November 1979 at Eric's Club in Liverpool; the first night of the "Future Pastimes Tour"; a "Fiction Records Package" tour featuring the Cure, the Passions and the Associates. He remained the Associates' bassist from 1979 to 1983, appearing on the albums "Fourth Drawer Down" (1981) and "Sulk" (1982) along with a number of singles between 1980 and 1983. He also performed with the group on a series of radio sessions recorded for Radio 1's John Peel and David Jensen shows, which were later released in 2003 as the album "Radio 1 Sessions Volume 1; 1981–83".