In certain surveillance applications it is imperative that the deployed Wireless Sensor Network (WSN) is not detected by the adversaries before the intruding party is detected by the WSN (i.e., the WSN is in the stealth mode of operation). Limiting the transmission ranges of sensor nodes is an option to mitigate the compromising privacy of the WSN (i.e., data communication within the WSN is not detected from far away). However, using all sensor nodes with minimal energy transmission level has devastating effects on the network lifetime because some nodes acting as relays are heavily burdened by conveying the data flowing from an unproportionately high number of sensor nodes. Such an approach will lead to the premature death of certain subset of sensor nodes. Alternatively, sensor nodes' transmission ranges can be limited as a function of their distance to the network border. Even under this policy a subset of the nodes become hotspots. On the other hand, nodes close the border cannot dissipate their energies completely because they cannot relay much data due the limits imposed on their transmission ranges. One possible solution to mitigate the uneven energy dissipation characteristic is to let the nodes that cannot dissipate their energies on communications reduce the amount of data they generate through computation so that the relay nodes convey less data. In this study we create a novel Linear Programming (LP) framework to model the energy cost of contextual privacy and multi-level data compression in WSNs.