The Rehr-Albers (RA) separable Green’s-function formalism, which is based on an expansion series, has been successful in speeding up multiple-scattering cluster calculations for photoelectron diffraction simulations, particularly in its second-order version. The performance of this formalism is explored here in terms of computational speed, convergence over orders of multiple scattering, over orders of approximation, and over cluster size, by comparison with exact cluster-based formalisms. It is found that the second-order RA approximation [characterized by $(6\mathrm{}\times 6)$ scattering matrices] is adequate for many situations, particularly if the initial state from which photoemission occurs is of s or p type. For the most general and quantitative applications, higher-order versions of RA may become necessary for d initial states [third-order, i.e., $(10\mathrm{}\times 10)$ matrices] and f initial states [fourth-order, i.e., $(15\mathrm{}\times 15)$ matrices]. However, the required RA order decreases as an electron wave proceeds along a multiple-scattering path, and this can be exploited, together with the selective and automated cutoff of weakly contributing matrix elements and paths, to yield computer time savings of at least an order of magnitude with no significant loss of accuracy. Cluster sizes of up to approximately 100 atoms should be sufficient for most problems that require about 5% accuracy in diffracted intensities. Excellent sensitivity to structure is seen in comparisons of second-order theory with variable geometry to exact theory as a fictitious “experiment.” Our implementation of the Rehr-Albers formalism thus represents a versatile, quantitative, and efficient method for the accurate simulation of photoelectron diffraction.