We consider the way in which antigen is presented to T cells on MHC molecules and ask how MHC peptide presentation could be optimized so as to obtain an effective and safe immune response. By analysing this problem with a mathematical model of T-cell activation, we deduce the need for both MHC restriction and high presentation selectivity. We find that the optimal selectivity is such that about one pathogen-derived peptide is presented per MHC isoform, on the average. We also indicate upper and lower bounds to the number of MHC isoforms per individual based on detectability requirements. Thus we deduce that an important role of MHC presentation is to act as a filter that limits the diversity of antigen presentation.