The mechanisms by which variations in the lipid composition of cell membranes influence the function of membrane proteins are not yet well understood. In recent work, a nonlocal thermodynamic mechanism was suggested in which changes in lipid composition cause a redistribution of lateral pressures that in turn modulates protein conformational (or aggregation) equilibria. In the present study, results of statistical thermodynamic calculations of the equilibrium pressure profile and bilayer thickness are reported for a range of lipids and lipid mixtures. Large redistributions of lateral pressure are predicted to accompany variation in chain length, degree and position of chain unsaturation, head group repulsion, and incorporation of cholesterol and interfacially active solutes. Combinations of compositional changes are found that compensate with respect to bilayer thickness, thus eliminating effects of hydrophobic mismatch, while still effecting significant shifts of the pressure profile. It is also predicted that the effect on the pressure profile of addition of short alkanols can be reproduced with certain unnatural lipids. These results suggest possible roles of cholesterol, highly unsaturated fatty acids and small solutes in modulating membrane protein function and suggest unambiguous experimental tests of the pressure profile hypothesis. As a test of the methodology, calculated molecular areas and area elastic moduli are compared with experimental and simulation results.