A B.C.S. type of theory (see BARDEEX, COOPER and SCHREIFFER, Phys. Rev. 108, 1175 (1957)) is sketched for very dirty superconductors, where elastic scattering from physical and chemical impurities is large compared with the energy gap. This theory is based on pairing each one-electron state with its exact time reverse, a generalization of the k up, -k down pairing of the B.C.S. theory which is ...