The interactions among a population of crystallites in a melt is studied, and the relation between the interactions and the system's volume fraction is established for small volume fractions. Through the solution of the diffusion analog of the Debye-Huckel equation, we obtain the growth rate of a crystal of specified radius. The growth rate reflects contributions from interactions among the crystal-melt interfaces, and is different from that predicted classically by Lifshitz and Slyozov. The crystallite size distribution, scaled by average crystal size, is obtained numerically through a solution to the continuity equation. We demonstrate that interactions among crystallites broaden the size distribution, and increase the coarsening rate. The new results reported for the coarsening rate and crystallite size distribution appear to be in good agreement with other theoretical and computer simulation results.