Many communications and networking systems can be modelled as resource-sharing systems with multiple classes of calls. Call admission control (CAC) is an essential component of such systems. For most practical systems it is prohibitively difficult to compute the optimal CAC policy that optimizes certain performance metrics because of the 'curse of dimensionality'. In this paper we study two families of structured CAC policies: threshold and reservation policies. These policies are easy to implement and have good performance in practice. However, since the number of structured policies grows exponentially with the number of call classes and the capacity of the system, finding the optimal structured policies is a complex unsolved problem. In this paper efficient search algorithms are proposed to find the coordinate optimal structured policies among all structured policies. Through extensive numerical experiments we show that the search algorithms converge quickly and work for systems with large capacity and many call classes. In addition, the returned structured policies have optimal or near-optimal performance, and outperform those structured policies with parameters chosen based on simple heuristics.