Positive selection is a process that ensures that peripheral T cells express TCR that are self-MHC restricted. This process occurs in the thymus and requires both self-MHC and self-peptides. We have recently established a TCR transgenic (TCR(trans)+) mouse model using the C10.4 TCR restricted to the MHC class Ib molecule, H2-M3. Having defined H2-M3 as the positively selecting MHC molecule, the severely limited number of H2-M3 binding peptides allowed us to characterize a mitochondrial NADH dehydrogenase subunit 1-derived 9-mer peptide as the physiological ligand of positive selection. Here, we demonstrate that the NADH dehydrogenase subunit 1 self-peptide is seen by mature C10.4 TCR(trans)+ T cells as a weak agonist and induces positive selection at a defined concentration range. We also found that the full-length cognate peptide, a strong agonist for mature C10.4 TCR(trans)+ T cells, initiated positive selection, albeit at significantly lower concentrations. At increased peptide concentrations, and thus increased epitope densities, either peptide only induced the development of partially functional T cells. We conclude that successful positive selection only proceeded at a defined, yet fairly narrow window of avidity.