We used three complementary techniques to vary the chemical potential of water in lipid/water mixtures; we measured the work of removing water from the multilayer lattice formed in water by the zwitterionic phospholipid egg lecithin. By x-ray diffraction, we observed the structural consequences of water removal. There are no discrete classes of "bound water" in this system; the work of removal is a continuous function of water content and lattice repeat spacing. From 30 to 3 A separation between bilayers there exists an exponential "hydration force" repulsion with a 2.6 A decay length. This interaction translates into a very large force to prevent contact between vesicles and planar membranes. It may be an important feature in controlling vesicle-to-cell fusion. As water is removed, bilayers not only move closer, but thicken as the lipid polar groups on the same bilayer move closer together. It is possible to divide the applied work into that of direct bilayer repulsion and that of bilayer deformation. We thus obtained a first determination of the lateral pressure required to create large increases in bilayer thickness and concomitant decreases in bilayer area. The lateral pressure reaches 25 dynes/cm for a 25% decrease in bilayer area. Systematic measurements of the mechanical properties of bilayers suffering such large deformation will allow critical tests of theories on bilayer stability and phase transition.