We consider the problem of gathering data from a wireless multi-hop network of energy-constrained sensor nodes to a common base station. Specifically, we aim to balance the total amount of data received from the sensor network during its lifetime against a requirement of sufficient coverage for all the sensor locations surveyed. Our main contribution lies in formulating this balanced data gathering task, studying the effects of balancing, and proposing an approximation algorithm for the problem. Based on an LP network flow formulation, we present experimental results on both optimal and approximate data routing designs, in open transmission ranges and with impenetrable obstacles between the nodes.