A key finding is that since the space of water models of interest describes relatively similar, near-physical phase spaces, we were able to accurately optimize over the entire space of models encountered in the optimization, using only reweighting from only a limited number of simulations at multiple temperatures and pressures. We specifically used simulations of SPC-E, OPC, TIP4P-EW, OPC3 and TIP3P, each of which have substantially different parameters and different deviations from the experiment, but all of which have relatively similar and good physical properties. With this relatively limited number of simulations, we could then use MBAR to accurately estimate the residual properties for the space of models that was minimized over, without carrying out additional simulations.