T-cells are activated when their receptor molecules recognize complexes of MHC proteins bound to peptides on the surface of neighbouring cells. Each T-cell expresses one variant of many possible receptor molecules, which are generated through a partially random process that culminates in approximately 107�possible T-cell receptors. As the peptide sequence bound to an MHC molecule is also highly variable, the optimal strategy of an antigen-presenting cell for displaying peptide-MHC complexes is not obvious. A natural compromise arises between aggressive peptide filtering, displaying a few peptides with high stability MHC binding in high abundance and regularity, and promiscuous peptide binding, which can result in more diverse peptides being presented, but in lower abundance. To study this compromise, we have combined a model of MHC class I peptide filtering with a simple probabilistic description of the interactions between antigen presenting cells (APCs) and cytotoxic Tcells (CTLs). By asking how long it takes, on average, for an APC to encounter a circulating CTL that recognises one of the peptides being presented by its MHC molecules, we found that there often exists an optimal degree of peptide filtering, which minimises this expected time until first encounter. The optimal degree of filtering is often in the range of values that the chaperone molecule tapasin confers on peptide selection, but varies between MHC class I molecules that have different peptide binding properties. Our model-based analysis therefore helps to understand how variations in the antigen presentation profile might be exploited for vaccine design or immunotherapies.