Up to this point the analysis has dealt with situations that fall into the category of standard Stefan problems, from now on we diverge from this by permitting changes in properties, such as the specific heat, density in each phase as well as the phase change temperature. The density jump between phases is often neglected but plays an important role – density change in confined spaces can cause damage while, in terms of the problem formulation, it induces motion in the fluid, which then introduces kinetic energy into the system. Consequently, when properties change, a new form of Stefan condition applies. Starting from conservation laws for mass, momentum, mechanical energy and total energy, a more general form for the governing equations is derived. It is shown how these may be reduced to apply to one-dimensional Cartesian and spherical problems. When the phase change temperature varies the simple one-phase Stefan problem is known to lose energy. This issue is explained and the energy conserving form presented.