We have accounted for the unusual structural change wherein dioleoylphosphatidylethanolamine undergoes a hexagonal-lamellar-hexagonal transition sequence as the water content is reduced systematically. We describe the role played by the energies of bending, hydration, voids in hexagonal interstices, and van der Waals interaction in this transition sequence. We have used the X-ray diffraction and osmotic stress experiments on the two phases to derive the structural parameters and all of the force constants defining the energetics of the hexagonal and lamellar phases. We have calculated the chemical potentials of lipid and water in both phases and derived the phase diagram of the lipid with no free, adjustable parameters. The calculated temperature/osmotic stress and temperature/composition diagrams quantitatively agree with experiment. The reentrant transition appears to be driven by a delicate balance between the hydration energy in the lamellar phase and bending energy in the hexagonal phase, whereas the energy of voids in hexagonal interstices defines its energy scale and temperature range. Van der Waals attraction between the bilayers in the lamellar phase does not appear to be important in this transition.