In a previous study we presented a new model of crystal growth from undercooled melts. This model demonstrated that the diffusion of the rejected volume at the crystal/liquid interface into the liquid phase could considerably change the kinetics of crystal growth from deeply undercooled liquids. In this article we present an analysis of crystal growth from undercooled liquids, paying close attention to the influence of the rejected free-volume on the grain size dependence on undercooling.