We have studied the conductance properties of unmodified monoglyceride membranes as a function of monoglyceride chain length. As membrane thickness decreases from 31 to 20 nm, the steepness of the current-voltage (I-V) curve increases from 80 mV per e-fold current increase to 52 mV per e-fold current increase. The zero-voltage conductance increases more than 1,000-fold and the apparent activation energy of conductance decreases from 18.4 to 14.2 kcal/mol. We have analyzed our results using both the Nernst-Planck equation and absolute rate theory. Both approaches are consistent with our results and give consistent values for the parameters describing the I-V curves. We conclude that both the surface ion concentration and the distance from the surface of the membrane at which the energy of an ion rises appreciably above its value in solution (position of the barrier) are invariant with thickness.