To gain insight into the molecular causes and functional consequences of allelic inclusion of TCR alpha-chains, we develop a computational model for thymocyte selection in which the signal that determines cell fate depends on surface expression. Analysis of receptor pairs on selected dual TCR cells reveals that allelic inclusion permits both autoreactive TCR and receptors not in the single TCR cell repertoire to be selected. However, in comparison with earlier theoretical studies, relatively few dual TCR cells display receptors with high avidity for thymic ligands because their alpha-chains compete aggressively for the beta-chain, which hinders rescue from clonal deletion. This feature of the model makes clear that allelic inclusion does not in itself compromise central tolerance. A specific experiment based on modulation of TCR surface expression levels is proposed to test the model.