The proliferation of mobile computing devices and lo- cal wireless networks has promoted a growing interest in location-aware systems. The problem with existing posi- tioning techniques is that they are designed to position di- mensionless objects. Such an assumption may lead to prac- tical inconsistencies, as objects might overlap in the result- ing 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 through- out 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 ap- proaches fail, the new considerations of VAPS do make a difference.