The maximum electron density and confinement time of Ohmically heated tokamaks can be limited by radiation losses. This has been investigated with a 1-D electron energy balance, used to derive current density distributions. Application of ideal-MHD stability criteria then leads to closed regions of stability in (I, ne)-space. Subsequent application of resistive-MHD theory indicates many possible causes of the disruptive instability and extends the ideal-MHD density limit by about 1.4 times. Murakami scaling, modified by a term involving the plasma effective charge , arises naturally from the model and suggests that results should be plotted in (q−1(a), (neR/Bt) )-space. Further, for heavy impurities, large divergences from Alcator scaling of τe are obtained within the stable region, leading to a peaking of τe versus ne at a critical density which scales as q−1 (a) Bt/R. The nτ-limit imposed by stability is found to further restrict the ignition region when referred to axial radiation losses only.