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The problem of cooperative data censoring in battery-powered multihop sensor networks is analyzed in this paper. We are interested in scenarios where nodes generate messages (which are related to the sensor measurements) that can be graded with some importance value. Less important messages can be censored in order to save energy for later communications. The problem is modeled using a joint Markov Decision Process of the whole network dynamics, and a theoretically optimal censoring policy, which maximizes a long-term reward, is found. Though the optimal censoring rules are computationally prohibitive, our analysis suggests that, under some conditions, they can be approximated by a finite collection of constant-threshold rules. A centralized algorithm for the computation of these thresholds is proposed. The experimental simulations show that cooperative censoring policies are energy-efficient, and outperform other non-cooperative schemes.