We have obtained spectroscopic redshifts of colour-selected point sources in four wide area VLT-FLAMES (Very Large Telescope-Fibre Large Array Multi Element Spectrograph) fields around the Fornax cluster giant elliptical galaxy NGC 1399, identifying as cluster members 27 previously unknown faint (-10.5<M_g'_<-8.8) compact stellar systems (CSS), and improving redshift accuracy for 23 previously catalogued CSS.