We review very strong selection effects which operate against the detection of dim (i.e. low surface brightness) galaxies. The Parkes multibeam instrument offers a wonderful opportunity to turn up new populations of such galaxies. However, to explore the newly accessible parameter space, it will be necessary to survey both a very deep patch (105 s/pointing, limiting Nhi ∼ 1018 cm−2) and a deep patch (104 s/pointing, limiting Nhi ∼ 3 × 1018 cm−2) in carefully selected areas, and we outline the case to do this.