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The proliferation of mobile computing devices and local wireless networks has promoted a growing interest in location-aware systems. The problem with existing positioning techniques is that they are designed to position dimensionless objects. Such an assumption may lead to practical inconsistencies, as objects might overlap in the resulting coordinate system. Moreover, it is usual to neglect the effects of an object volume and its physical characteristics on signal propagation. In the scenario considered throughout this paper (positioning containers in a harbor), such characteristics can be finely estimated. We propose VAPS, a volume-aware positioning system that takes advantage of the waveguide effect generated by containers. Although VAPS is specific to the harbor scenario, its principles can be extended and adapted to other situations. VAPS maps discrete RSSI levels into hop-counts and relies on realistic propagation models to obtain near-perfect positioning at a very low control overhead. Our results demonstrate that, in scenarios where the assumptions made by traditional approaches fail, the new considerations of VAPS do make a difference.