For many years, density-functional-based calculations for the total energies of substitutionally disordered alloys have been based upon the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA). However, as a result of the single-site nature of the KKR-CPA, such calculations do not take into account important local environmental effects such as charge correlations (the Madelung energy) and chemical short-range order (SRO). Here the above approach is generalized by combining the recently developed Korringa-Kohn-Rostoker nonlocal coherent-potential approximation with density functionl theory, showing how these effects may be systematically taken into account. As a first application of the theory, total energy calculations for the bcc CU₅0Zn₅0 solid solution are presented, showing how the total energy varies as a function of SRO. The fcc Cu₆0Pd₄0 and Cu77Ni₂3 systems are also investigated.