Exceptions to the Meyer-Overton rule are commonly cited as evidence against indirect, membrane-mediated mechanisms of general anesthesia. However, another interpretation is possible within the context of an indirect mechanism in which solubilization of an anesthetic in the membrane causes a redistribution of lateral pressures in the membrane, which in turn shifts the conformational equilibrium of membrane proteins such as ligand-gated ion channels. It is suggested that compounds of different stiffness and interfacial activity have different intrinsic potencies, i.e., they cause widely different redistributions of the pressure profile (and thus different effects on protein conformational equilibria) per unit concentration of the compound in the membrane. Calculations incorporating the greater stiffness of perfluoromethylenic chains and the large interfacial attraction of hydroxyl groups predict the higher intrinsic potency of short alkanols than alkanes, the cutoffs in potency of alkanes and alkanols and the much shorter cutoffs for their perfluorinated analogues. Both effects, increased stiffness and interfacial activity, are present in unsaturated hydrocarbon solutes, and the intrinsic potencies are predicted to depend on the magnitude of both effects and on the number and locations of multiple bonds within the molecule. Most importantly, the intrinsic potencies of polymeric alkanols with regularly spaced hydroxyl groups are predicted to rise with increasing chain length, without cutoff; such molecules should serve to distinguish unambiguously between indirect mechanisms and direct binding mechanisms of anesthesia.