Sedimentation of charged silica spheres in ethanol has been studied as a function of ionic strength and volume fraction phi. It is shown for the first time by experiment that at very low ionic strength the normalized sedimentation velocity U/U-0 follows a remarkable phi dependence of the form 1 - p phi(1/3), which leads to a strong decrease in U/U-0 at very low concentrations. This dependence agrees with theoretical calculations of the sedimentation velocity. The calculated numerical coefficient p, however, is smaller than the experimental value. Both experiments and calculations show that addition of salt gradually changes the phi(1/3) dependence to the linear phi dependence characteristic for hard spheres. The phi(1/3) behavior for salt-free dispersions renders it very difficult to measure quantities at "infinite dilution."