By applying a new method for solving the equations of the relativistic Korringa-Kohn-Rostoker-coherent-potential approximation. The authors have been able to study the electronic structure of compositionally disordered Pd-Pt alloys. This investigation was carried out, on the one hand, to test the reliability of the method itself and, on the other, to learn whether a 'rigid band' picture is appropriate for these alloys as suggested by an interpretation of residual resistivity measurements. They find that the method is numerically stable and can now be safely incorporated into a self-consistent-field local-density theory for alloys with heavy elements. Moreover, the electronic structure of Pd-Pt is found to be 'non-rigid-band' like and demonstrates some interesting new features arising from mass-velocity, Darwin and spin-orbit coupling effects.