We address the occurrence of conduction-band crossover in III-V self-assembled quantum dots solely due to misfit strain. Band structure analysis in terms of standard deformation-potential theory shows that ⌫-X crossover can occur in the dot, while both ⌫-X and ⌫-L crossovers are possible in the matrix at the interface. Crossover changes the nature of the fundamental band gap in the heterostructure, which may dramatically affect the optical properties. The implications of this are studied for a realistic InSb/ GaSb ͑001͒ heterostructure, where ⌫-L crossover renders the ground-state optical transition indirect in k space. Our calculations and photoluminescence data are in remarkable agreement.