Diffusion is the implicit null hypothesis for ion transport across biological membranes. A proper model of ionic diffusion across the permeability barrier is needed to distinguish among leaks, channels and carriers and to determine whether changes in flux reflect changes in permeability (regulation) or merely changes in the driving force. These issues arise in all biomembranes, but they are particularly confounding in energy-transducing membranes on account of their characteristically high electrical gradients. This paper examines the nature of the barrier to ion leaks, using the classical Eyring rate theory. We introduce new practical procedures for estimating permeability coefficients from ion flux data. We also reach some general conclusions regarding ion leaks across energy-transducing membranes. (1) The dependence of ion flux on the electrical membrane potential is invariably non-linear (non-ohmic). (2) Non-ohmic behavior does not imply variable permeability. (3) Ohmic behavior is exceptional and its occurrence should alert us to the possibility of an underlying carrier or channel. (4) Leak pathways are very likely localized to protein-lipid interfaces and will exhibit quasi-specific properties such as saturation and competition. (5) The inherent non-ohmicity of leaks and the requirement for efficient energy transduction impose constraints upon the magnitude of allowable Gibbs free-energy changes in biological systems. (6) Nature adapts to these constraints by devising mechanisms for step-wise splitting of the partial reactions of energy transduction.