The CD8 coreceptor modulates the interaction between the T cell antigen receptor (TCR) and peptide-major histocompatibility class I (pMHCI). We present evidence that CD8 not only modifies the affinity of cognate TCR/pMHCI binding by altering both the association rate and the dissociation rate of the TCR/pMHCI interaction, but modulates the sensitivity (triggering threshold) of the TCR as well, by recruiting TCR/pMHCI complexes to membrane microdomains at a rate which depends on the affinity of MHCI/CD8 binding. Mathematical analysis of these modulatory effects indicates that a T cell can alter its functional avidity for its agonists by regulating CD8 expression, and can rearrange the relative potencies of each of its potential agonists. Thus we propose that a T cell can specifically increase its functional avidity for one agonist, while decreasing its functional avidity for other potential ligands. This focussing mechanism means that TCR degeneracy is inherently dynamic, allowing each TCR clonotype to have a wide range of agonists while avoiding autorecognition. The functional diversity of the TCR repertoire would therefore be greatly augmented by coreceptor-mediated ligand focussing.