The authors considered the coherent potential approximation (CPA) for a substitutionally disordered alloy crystal potential which is of the nonoverlapping muffin-tin form. The authors simplified the KKR-CPA theory using the atomic sphere approximation (ASA) of Andersen (1975). In its new form the fundamental equations of the theory can be solved numerically. The computational effort is not particularly large on the scale of modern bandstructure calculations. As an illustration of the authors' method they calculated the Bloch spectral functions and the partially averaged local density of states for a number of alloy potentials designed to represent paramagnetic Cu_cNi_1-c alloys. Where comparison is possible the authors found good agreement with previous calculations. Their results are also consistent with various experimental data.