We consider an environment where distributed data sources continuously stream updates to a centralized processor that monitors continuous queries over the distributed data. Significant communication overhead is incurred in the presence of rapid update streams, and we propose a new technique for reducing the overhead. Users register continuous queries with precision requirements at the central stream processor, which installs filters at remote data sources. The filters adapt to changing conditions to minimize stream rates while guaranteeing that all continuous queries still receive the updates necessary to provide answers of adequate precision at all times. Our approach enables applications to trade precision for communication overhead at a fine granularity by individually adjusting the precision constraints of continuous queries over streams in a multi-query workload. Through experiments performed on synthetic data simulations and a real network monitoring implementation, we demonstra...