Discretized population balances of aggregating systems are known to consistently over-predict number densities for the largest particles. This over-prediction has been attributed recently by the authors (Kumar and Ramkrishna, 1996, Chem. Engng Sci. 51, 1311-1332) to steeply non-linear gradients in the number density when a fixed pivotal particle size is used for each discrete interval. The present work formulates macroscopic balances of populations with due regard to the evolving non-uniformity of the size distribution in each size interval as a result of breakage and aggregation events. This is accomplished through a varying pivotal size for each interval adapting to the prevailing non-uniformity of the number density in the interval. The technique applies to a general grid and preserves any two arbitrarily chosen properties of the population. Comparisons of the numerical and analytical results have been made for pure aggregation for the constant, sum and product kernels. It is established that numerical predictions from macroscopic balances are significantly improved by an adapting pivot accounting for non-uniformities in the number density.