The uncertainty management problem is one of the key issues associated with moving objects (MOs). Minimizing the uncertainty region size can increase both query accuracy and system performance. In this paper, we propose an uncertainty model called the Truncated Tornado model as a significant advance in minimizing uncertainty region sizes. The Truncated Tornado model removes uncertainty region sub-areas that are unreachable due to the maximum velocity and acceleration of the MOs. To make indexing of the uncertainty regions more tractable we utilize an approximation technique called Tilted Minimum Bounding Box (TMBB) approximation. Through experimental evaluations we show that Truncated Tornado in TMBB results in orders of magnitude reduction in volume compared to a recently proposed model called the Tornado model and to the standard "Cone" model when approximated by axis-parallel MBB.