We describe a search for compact dwarf galaxies in the Fornax cluster using the FLAIR spectrograph on the UK Schmidt Telescope . We measured radial velocities of 453 compact galaxies brighter than B _ { T } \approx 17.3 and found seven new compact dwarf cluster members that were not classified in previous surveys as members of the cluster . These are amongst the most compact , high surface brightness dwarf galaxies known . The inclusion of these galaxies in the cluster does not change the total luminosity function significantly but they are important because of their extreme nature ; one in particular appears to be a high ( normal ) surface brightness dwarf spiral . Three of the new dwarfs have strong emission lines and appear to be blue compact dwarfs ( BCDs ) , doubling the number of confirmed BCDs in the cluster . We also determined that none of the compact dwarf elliptical ( M32-like ) candidates are in the cluster , down to an absolute magnitude \hbox { { M } $ { } _ { B } $ } = -13.2 . We have investigated the claim of Irwin et al . ( 1990 ) that there is no strong relation between surface brightness and magnitude for the cluster members and find some support for this for the brighter galaxies ( B _ { T } < 17.3 ) but fainter galaxies still need to be measured .