Sensor networks consist of battery-powered wireless devices that are required to operate unattended for long periods of time. Thus, reducing energy drain is of utmost importance when designing algorithms and applications for such networks. Aggregate queries are often used by monitoring applications to assess the status of the network and detect abnormal behavior. Since radio transmission often constitutes the biggest factor of energy drain in a node, in this paper we propose novel algorithms for the evaluation of bandwidthconstrained queries over sensor networks. The goal of our techniques is, given a target bandwidth utilization factor, to program the sensor nodes in a way that seeks to maximize the accuracy of the produced query results at the monitoring node, while always providing strong error guarantees to the monitoring application. This is a distinct difference of our framework from previous techniques that only provide probabilistic guarantees on the accuracy of the query result. Our algorithms are equally applicable when the nodes have ample power resources, but bandwidth consumption needs to be minimized, for instance in densely distributed networks, to ensure proper operation of the nodes. Our experiments with real sensor data show that bandwidth-constrained A. Deligiannakis (B)