The steady-state transport-limited voltammetry of ions has been modelled in the presence of excess supporting electrolyte and in its total absence. As expected, oxidation of a cation (or reduction of an anion) is predicted to result in a decrease in the limiting current when supporting electrolyte is removed. Alternatively, reduction of a cation (or oxidation of an anion) is predicted to result in an increase in the limiting current when supporting electrolyte is removed. When the product is an ion, its presence and that of the counter-ion diminish the importance of reactant migration, leading to the prediction that the limiting current will differ from that in the presence of excess supporting electrolyte by a known factor not very different from unity. Greater differences from unity are predicted when the number of electrons transferred in the electrode reaction becomes quite large or when the product is neutral. The model has been tested using a wide variety of reactions, comprising reductions of anions and both oxidations and reductions of cations. In the majority of cases the agreement with prediction is remarkably good. In many other cases, however, waves which are observed when excess supporting electrolyte is present almost disappear in its absence. At present we have no credible explanation for this phenomenon. The voltammetric waves generally satisfy the Tomes criterion of reversibility, confirming that the IR drop is small.