Nonempirical phase diagram calculations were performed for one A(B′,B′′)O3, and two [A', A'']BO3 perovskite-based systems: Pb(Sc1/2Ta1/2)O3-PbTiO3, PbTiO3-CaTiO3, and PbTiO3-SrTiO3. In addition, total energy calculations were performed for some other A(B', B'')O3 and [A', A'']BO3 systems. Cluster expansion Hamiltonians were derived from Potential Induced Breathing (PIB) total energy calculations for large supercells (up to 80 atoms), and then used as input for cluster variation method (CVM) phase diagram calculations. These calculations give general insight into the thermodynamics of solid solutions that are based on coupled substitution and into the limits of the computational approach. In addition, spherical self consistent atomic deformation (SSCAD) total energy calculations were performed for several Pb(Mg1/3Nb2/3)O3, and Ba(Zn1/3Ta2/3)O3 supercell configurations. Also presented, are the results of a neutron powder difraction study of cation ordering in a [Pb0.5469 Ca0.4531]TiO3 sample.