In phase-change problems, there are domain and surface contributions to the dynamics of a moving front. It is ordinarily assumed that the surface contributions are in complete control. This is likely to be true in the case of planar fronts, but it may or may not be true in the cylindrical case. We study the growth rates of disturbances imposed on the surface of a cylindrical solid in equilibrium with its melt and deduce the conditions under which time derivatives of bulk-phase variables are important. They are important in the case of a whisker and are even more important if a solute is added.