Epitopes presented by major histocompatibility complex (MHC) class I molecules are selected by a multi-step process. Here we present the first computational prediction of this process based on in vitro experiments characterizing proteasomal cleavage, transport by the transporter associated with antigen processing (TAP) and MHC class I binding. Our novel prediction method for proteasomal cleavages outperforms existing methods when tested on in vitro cleavage data. The analysis of our predictions for a new dataset consisting of 390 endogenously processed MHC class I ligands from cells with known proteasome composition shows that the immunological advantage of switching from constitutive to immunoproteasomes is mainly to suppress the creation of peptides in the cytosol that TAP cannot transport. Furthermore, we show that proteasomes are unlikely to generate MHC class I ligands with a C-terminal lysine residue, suggesting processing of these ligands by a different protease that may be tripeptidyl-peptidase II (TPPII).