In many cases, the resolution provided by capillary electrophoresis systems approaches that predicted for diffusion-limited separations. Once all device-related sources of band broadening have been eliminated or minimized, only thermal diffusion remains. In principle, peaks can be sharpened using gradients of various system characteristics such as gel concentration, buffer viscosity and electric field. However, it is not clear whether this can actually increase the resolution of the system. In this article, we focus our attention on viscosity gradients and we examine both continuous and step-like variations. Our results indicate that the performance of electrophoretic systems cannot be improved by viscosity gradients. They may provide extra stacking, and thus improve the resolution, when the injection width is non-negligible. However, for the systems considered here, the best resolution is obtained when the viscosity is uniform and the stacking is entirely performed at injection. We conclude by discussing the link between these results, the fundamental laws of thermodynamics, the nature of the detection process and the importance of having nonlinear effects in nonuniform systems.