4. We have performed break-junction Josephson-effect measurements in BSCCO and BSCO (Bi2Sr2CuO6+x) single crystals where, for the first time, the Josephson critical current Ic was measured as a function of temperature up to Tc. The large deviations of the Ic(T) from the BCS behaviour have been fully explained by a new model we developed, that takes into account the depression of the order parameter at the surfaces in a high-Tc Superconductor-Insulator-Superconductor (SIS) junction. The SIS depressed-gap model has been extended to the case of SIS' junctions, where S' is a conventional low-Tc superconductor, and the theoretical results have been compared to the experimental Ic(T) obtained in multilevel edge junctions YBa2Cu3O7+x/SrTiO3/ YBa2Cu3O7+x and in planar tunnel junctions YBa2Cu3O7+x/native barrier/Pb. Both in the planar junctions and in our break junctions, the depressed-gap model can accurately reproduce the deviations of the critical current from the BCS model, both in shape and magnitude, while a model that explains the same Ic(T) deviations in YBCO junctions by assuming an s + id pair symmetry with a dominant d-wave component needs additional hypotheses to do the same.