We present an approach to calculate free energy and other thermodynamic property differences between molecules which have very little or no overlap in configuration space, but where a one-to-one mapping between the molecule geometries exists. The approach combines multistate reweighting with remapping of phase space between simulated states. We apply this method to calculate the free energy differences between non-overlapping, truncated harmonic oscillators, the free energy, enthalpy, and entropy differences between different parameterizations of rigid water, and differences in free energy of solvation between dipoles of different lengths. Previously difficult or impossible problems become either trivially easy or are improved in efficiency by two to five orders of magnitude.