We report on the effects of hydrostatic pressure and temperature on the phase and structural behavior of the complete range of the known, excess water, inverse lyotropic mesophases. This range of interfacial topologies is exhibited by homologous series of saturated C-12, C-14, and C-16 dialkyl phosphatidylethanolamines (PE) and saturated C-12 and C-16 dialkyl xylopyranosylglycerols (xylolipids) in the p-T region 0-2.5 kbar and 30-130 degrees C. The PEs cover the mesophases with gentle interfacial curvature while the xylolipids cover the more curved mesophases. We demonstrate that temperature and pressure have noncongruent effects on the structural and the phase behavior. Quantitatively, mesophase lattice parameters and phase boundaries show small but observable differences in their functional dependence on pressure and temperature. Qualitatively, increasing pressure stabilizes inverse bicontinuous cubic phases in C-14 PE At atmospheric pressure only the C-12 PE contains such phases. Conversely we find that increasing pressure destabilizes the inverse micellar cubic phase observed in the C-16 xylolipid. In general a trend is seen for a stronger pressure effect in eliminating phases with larger packing costs, which we infer is due to differences in the effects of pressure and temperature on the monolayer’s spontaneous mean curvature and its bending rigidity.