The hydrostatic-pressure shifts of the Z1,2 and Z3 exciton peaks were measured in thin films of cubic CuCl, CuBr, and CuI at 90 K. That of the E1 peak in CuI also was measured. The deformation potentials of all Z excitons and of the E1exciton in CuI, about -1 eV, are more than twice those of the Z excitons in CuCl and CuBr. This suggests the two valence bands in CuI may be considerably more mixed than in CuCl and CuBr.