This paper examines the effect of diffusive interactions, and the correlations they create between particles, on Ostwald ripening. The effect accounts for a persistent discrepancy between theory and experiment, in which the distribution of particle sizes has been more broad and flat than mean-field theory predicts. A new model system is proposed to study the problem, and a hierarchy of equations derived from it is expanded in powers of the square root of the volume fraction. The time devlopment of correlations is analyzed through an unusual perturbation theory. The resulting differential equations are solved numerically and compared with experiment.