[en] A new model is proposed to describe the non-Arrhenius conductivity observed in a series of optimized fast ion-conducting silver thioborosilicate glasses. Its essential feature is that the mobile cations are thought to conduct from one open site to the next open available site and, in this process, naturally by-pass filled or unavailable sites. The thermal excitation of cations out of their equilibrium sites is taken to be the mechanism for generating the open and available anion sites. Hence, the mean free path for a drifting cation between open available sites is directly proportional to the activated carrier concentration and is therefore a strong function of temperature. There is also a weak temperature dependence for the mean free path that arises because the capture cross section for a drifting cation by a stationary anion trap varies with drift velocity, e.g. the momentum of a fast cation allows it to closely approach an anion trap while avoiding capture or back scattering. The capture cross section of a cation by an anion trap is large because the interaction is electrostatic rather than geometric in origin. The model is shown to be in good agreement with all of our experimental data for silver thioborosilicate glasses and all model parameters are physically defined and reasonable in value. The model predicts a simple high-temperature conductivity dependence that is not exponential in nature. The model is also proposed to be valid for other materials such as crystalline conductors