By Monte Carlo simulation we investigate a model where ions are diffusing in the presence of randomly placed, immobile counterions. All Coulombic effects are taken into account. Calculations of dc- and ac-transport properties in a range of temperatures and ion concentrations show that our counterion model can qualitatively explain several experimental features common to glassy ionic conductors, including the characteristic concentration-dependence of the dc-activation energy, the Haven ratio and also the frequency-dispersion in the ac conductivity. We also present some preliminary simulation results for the nuclear-spin lattice relaxation rate T1(-1).