The molal conductivity of liquid electrolytes with low static dielectric constants (epsilon(s) < 10) decreases to a minimum at low concentrations (region I) and increases to a maximum at higher concentrations (region when plotted against the square root of the concentration. This behavior is investigated by applying the compensated Arrhenius formalism (CAF) to the molal conductivity, Lambda, of a family of 1-alcohol electrolytes over a broad concentration range. A scaling procedure is applied that results in an energy of activation (E-a) and an exponential prefactor (Lambda(0)) that are both concentration dependent It is shown that the increasing molal conductivity in region II results from the combined effect of (1) a decrease in the energy of activation calculated from the CAF, and (2) an inherent concentration dependence in the exponential prefactor that is partly due to the dielectric constant.