Previously developed procedures that simulate the radiatively induced tokamak density limit are used to examine the scaling of the density limit in more detail. The maximum allowable density increases with auxiliary power and decreases with impurity concentration. However, there is little dependence of the density limit on plasma elongation. These trends are consistent with experimental results. Previous work used coronal equilibrium impurities; the primary result was that the maximum density increases with current when peaked profiles are assumed. Here, this behavior is shown to occur with a coronal nonequilibrium impurity as well.