Maintaining statistics on multidimensional data distributions is crucial for predicting the run-time and result size of queries and data analysis tasks with acceptable accuracy. To this end a plethora of techniques have been proposed for maintaining a compact data “synopsis” on a single table, ranging from variants of histograms to methods based on wavelets and other transforms. However, the fundamental question of how to reconcile the synopses for large information sources with many tables has been largely unexplored. This paper develops a general framework for reconciling the synopses on many tables, which may come from different information sources. It shows how to compute the optimal combination of synopses for a given workload and a limited amount of available memory. The practicality of the approach and the accuracy of the proposed heuristics are demonstrated by experiments.