Although the thymus produces many immature thymocytes, few of these cells mature. Positive selection has been thought to limit thymocyte development. In thymuses expressing a single MHC/peptide combination, however, surprisingly large numbers of thymocytes are selected to mature. Many of these react with the selecting MHC, bound to other self-peptides. Therefore, the number of thymocytes that mature is limited by the fact that positively selected cells die because they react too well with MHC bound to self-peptides that are not identical to those involved in positive selection. T cells that mature in thymuses expressing a single MHC/peptide ligand react frequently with foreign MHC, suggesting that the repertoire of alpha beta receptors may be more biased toward reaction with MHC than was previously thought.