Order-disorder phenomena on the simple-cubic B-site sublattice in A(B1/3B'2/3)O3 perovskites is examined. A simple cubic groundstate analysis in the cube approximation reveals that this approximation is inadequate for A(B1/3B'2/3)O3 perovskites, because it cannot predict a common experimentally-observed  superstructure. A partial vertex enumeration technique is used to demonstrate that a 12 interaction subset of the cube + linear triplet approximation is sufficient. First-principles calculations were performed for Ba(Zn1/3Ta2/3)O3 (BZT) and Pb(Mg1/3Nb2/3)O3 (PMN), two technologically interesting materials, in an effort to construct generalized Ising model Hamiltonians to enable simulations of these materials. Both ionic model (SSCAD) and pseudopotential (PP) calculations were done, enumerating the relative energies of a series of B-site superstructures. Structural hierarchies are reasonble and predict the  groundstate for both BZT and PMN, despite the fact that it is not observed in the latter. The pseudopotential results also indicate the possibility of metal-insulator transitions in BZT as a function of B-site configuration.