This work explores performance vs. communication energy tradeoffs in wireless sensor networks that use the recently proposed cutset deployment strategy in which sensors are placed densely along a grid of intersecting lines. For a given number of sensors, intersensor spacing is less for a cutset network than for a conventional lattice deployment, so that cutset networks require less communication energy, albeit with some potential loss in network performance. Previous work analyzed the energy-performance tradeoffs for square-grid cutset networks in the context of specific decentralized algorithms for source localization based on received signal strength (RSS). The current work also considers the RSS based source localization problem. However, it takes a more fundamental approach to analyzing the tradeoff by considering a centralized task, minimum energy communication paths, Maximum Likelihood estimation algorithms and Cramér-Rao bounds. Moreover, it analyzes triangular and honeycomb cutset deployments, in addition to square-grid ones. The results indicate that cutset networks offer sizable decreases in energy with only modest losses of performance.Index Terms-Wireless sensor networks, source localization.