A simple method is proposed for applying the self-consistent boundary site approximation (SCBSA) in cluster theories of electronic states in disordered alloys. This method is applicable to lattices of any dimensionality. The electronic densities of states are calculated for binary alloys having the simple cubic and the diamond lattice structures. These results are compared with the results obtained from the method of moments, the disordered field formalism, the coherent-potential approximation and a few other methods. In addition to this, the averaged Green's function has been calculated in the complex energy plane to study its analytic structure. It is found that though the SCBSA is computationally simple and yields densities of states which agree quite well with the available exact results, in three dimensions, the SCBSA shows some unphysical features such as the negative partial densities of states and branch points off the real axis for the averaged Green's function in the strong-scattering regime. {\textcopyright} 1978 The American Physical Society.