Given a region qR and a future timestamp qT, a "range aggregate" query estimates the number of objects expected to appear in qR at time qT. Currently the only methods for processing such queries are based on spatio-temporal histograms, which have several serious problems. First, they consume considerable space in order to provide accurate estimation. Second, they incur high evaluation cost. Third, their efficiency continuously deteriorates with time. Fourth, their maintenance requires significant update overhead. Motivated by this, we develop Venn sampling (VS), a novel estimation method optimized for a set of "pivot queries" that reflect the distribution of actual ones. In particular, given m pivot queries, VS achieves perfect estimation with only O(m) samples, as opposed to O(2m) required by the current state of the art in workload-aware sampling. Compared with histograms, our technique is much more accurate (given the same space), produces estimates with negligible cost, and does not deteriorate with time. Furthermore, it permits the development of a novel "query-driven" update policy, which reduces the update cost of conventional policies significantly.