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We study the problem of constructing a data gathering tree over a wireless sensor network in order to minimize the total energy for compressing and transporting information from a set of source nodes to the sink. This problem is crucial for advanced computationally intensive applications, where traditional "maximum" in-network compression may result in significant computation energy. We investigate a tunable data compression technique that enables effective trade-offs between the computation and communication costs. We derive the optimal compression strategy for a given data gathering tree and then investigate the performance of different tree structures for networks deployed on a grid topology, as well as general graphs. Our analytical results pertaining to the grid topology and simulation results pertaining to the general graphs indicate that the performance of a simple greedy approximation to the Minimal Steiner Tree (MST) provides a constant-factor approximation for the grid topology and good average performance on the general graphs. Although, theoretically, a more complicated randomized algorithm offers a polylogarithmic performance bound, the simple greedy approximation of MST is attractive for practical implementation.