Molecular dynamics simulations of sodium iodide dissolved in dimethyl ether or 1,2-dimethoxyethane (glyme) were studied at a range of salt concentrations. The interactions among the species were, represented with Lennard-Jones and Coulomb forces. Dimethyl ether and glyme were represented by a rigid three-site model and a six-site model with flexible dihedral angles, respectively. Glyme is demonstrated to be it much better solvent than dimethyl ether, although both are low-dielectric solvents. At the highest concentration studied in glyme, which corresponds to an oxygen/cation ratio of 16:1, free ions make up about 50% of the total ion concentration, and neutral pairs make up about 20%. A quantitative analysis of the species important in conductivity shows that the current is primarily the result of the movement of free ions and the relative movement of ions within loosely bound ion pairs. At higher salt concentrations, many different ionic species can make contributions; to the conductivity.