In a previous paper [J. Appl. Phys. 82, 3783 (1997)] we presented an analysis of the stability of a dendrite against a small perturbation to the tip velocity. This model demonstrated that dendritic growth in pure metals and alloys would become unstable above some upper critical undercooling ΔT2*, while in alloys above a critical concentration, dendritic growth may also become unstable below a lower critical undercooling, ΔT1*. However, quantitative agreement between the example system studied, Ni–Cu, and the available data was poor. In this article we present an improved computational scheme which allows us to relax the assumption that dendrites propagate as isothermal paraboloids of revolution. This results in much improved agreement with the experimental data.