A numerical model is used to study compositional profiles formed by cation exchange and diffusion at constant cooling rates in spherical mineral grains. Fe-Mg zoning in garnet-olivine pairs is used as an example. Zoned concentration profiles can be described by an exponential function; changes in the parameters of the function can be used to evaluate the effects of changes in inclusion size, cooling history, diffusion parameters, and exchange enthalpy. The composition of an olivine inclusion within garnet depends strongly on inclusion size due to finite volume effects, as does zoning in the garnet surrounding the inclusion. Thus estimates of equilibration temperatures obtained from small inclusions of one phase within another require a size correction. However, for a spherical garnet within an olivine matrix, the effect is small for garnet radii greater than 1000 μm. The shapes of zoned concentration profiles are useful for bounding both the rate of cooling and the final temperature. In addition, the concentration ratios (Fe garnet)/(Fe olivine) may be used to estimate the cooling rate once the final temperature is bounded.