The variational principle of Kohn and Rostokcr (KR) implies that the determinant of a product of matrices vanishes at energy eigenvalues. The standard KKR method uses square matrices appropriate to a truncated spherical harmonic expansion, and sets the determinant of one matrix in this product to zero. For general nonspherical potentials in space-filling local cells, the KR variational principle requires these matrices to be rectangular, since the intermediate sum should extend over a complete set of solid harmonic functions. If extended in this way, the intermediate sum can be replaced by a Wronskian surface integral over the interfaces of adjacent space-filling atomic cells, as formulated in the variational principle of Schlosser and Marcus. E-quivalence of these two different variational principles is established here in the limit of completeness of the intermediate sum. The practical implication is that the standard KKR method is not well founded for the full-potential problem. Improved results for low-order basis function expansions can be obtained by including a Wronskian interface integral in full-potential ACO calculations, as a variational completion of the truncated intermediate K KR sum. A revision of CPA alloy theory is proposed that avoids dependence on this intermediate sum.