CD8 positive lymphocytes (TCD8+) play an important role in host immunity to viruses and other intracellular parasites. Anti-viral TCD8+ recognize MHC class I molecules bound to peptides derived from a cytosolic pool of viral proteins. One of the curious features of TCD8+ responses to viral infections is that it typically focuses on a highly limited set of peptides. To better understand this phenomenon, we examined all of the nonameric peptides encoded by the influenza virus A/Puerto Rico/8/34 conforming to the canonical Kd binding motif. Among these 26 peptides, 10 bound strongly to Kd, including the two known antigenic peptides. Using recombinant vaccinia viruses encoding cytosolic or ER-targeted forms of these ten peptides, we found that the highly limited Kd-restricted response to influenza virus reflects in order of decreasing importance, class I binding affinity (although the immunodominant peptides rank only 2nd and 5th in relative binding affinity of those tested), peptide liberation by cellular proteases, diversity of TCR repertoire, and lastly, TAP mediated peptide transport. We also observed an additional important contributing factor: suppression of T cell responses to non-dominant peptides by an immunodominant peptide located in the same protein.