In order to avoid the computational expense required to obtain precise numerical solutions of the Poisson-Boltzmann equation, different hypotheses have been introduced which led to less rigorous, but fast and simple solvation models. However, few systematic studies of the predictive features of such models have been reported. Comparisons between different continuum models are made difficult by the large variety of simplifying hypotheses or thermodynamic reference states used by their authors, so that the relationships between the proposed solvation terms is not straightforward. In the present work we consider various continuum models whose common feature is the description of the solvation process in terms of displacement of the high dielectric solvent by the low dielectric molecular bulk. We adapt these different models to work within the frame of the nonlinear fit algorithm developed in our previous study. This leads to a benchmark allowing to run rigorous comparative tests between all the different schemes. The unification of these allows us to derive new solvent models that combine the advantages of the original ones. We address also the problem df the optimal parametrization of the solvation terms and propose a new strategy of assignment of the atomic radii. It is shown that the exact solvation energies, which are in theory linearly related to the solvent displacement terms, cannot be expressed as a linear combination of the displacement effects evaluated with the usual simplifications. Nevertheless, nonlinear empirical models based on these simplified displacement terms are found to yield high quality predictions of vacuum-to-water transfer energies.