The rapid proliferation of mobile computing devices and local wireless networks over the past few years has promoted a continuously growing interest in location-aware systems and applications. The main problem with existing positioning techniques is that they are designed to position dimensionless objects. Such an assumption may lead to practical inconsistencies, as it results in neglecting the effects of the volume of an object, its physical characteristics, and its spatial arrangement on signal propagation. In this paper, we consider the problem of positioning cargo containers in a marine port terminal, where such characteristics can be finely estimated. Based on the signal propagation map of a container yard, we propose VAPS, a volume-aware positioning system that takes advantage of the waveguide effect generated by the containers. Although VAPS is specific to the marine port scenario, its design 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 extensive evaluations show how to set the parameters required in the VAPS algorithm. The results demonstrate that, in scenarios where the assumptions made by traditional approaches fail, the considerations of VAPS make the difference.