The TCR alpha-chain is assembled by somatic recombination of variable (V) and joining (J) gene segments at the CD4+ CD8+ stage of development. In this study, we present the first analytical model for deletional rearrangement and show that it is consistent with almost all available data on Valpha Jalpha use in mice and humans. A key feature of the model is that both "local" and "express service" models of rearrangement can be obtained by varying a single parameter that describes the number of gene segments accessible at a time. We find that the window is much larger for Valpha segments than Jalpha segments, which reconciles seemingly conflicting data for the former. Implications for the properties of the repertoire as a whole and experiments that seek to probe them are discussed. Special considerations for allelic inclusion are treated in the Appendices.