— Recent advances in energy harvesting devices and low-power embedded systems are enabling energetically self-sustainable wireless sensing systems able to sense, process, and wirelessly transmit environmental data. In such systems, energy resources need to be judiciously allocated to processing and transmission tasks to guarantee high-fidelity reconstruction of the phenomenon under observation while keeping the system operational over extended periods of time. Within this context, this paper addresses the problem of designing efficient policies to control the task of lossy data compression for wireless transmission over fading channels in the presence of a stochastic energy input process and a replenishable energy buffer. As a first contribution, the transmission and energy dynamics of a sensor node implementing practical lossy compression methods are modeled as a Constrained Markov Decision Problem (CMDP). Then, an algorithm is designed to derive optimal compression/transmission ...