A key function of a host-based intrusion detection system is to monitor program execution. Models constructed using static analysis have the highly desirable feature that they do not produce false alarms; however, they may still miss attacks. Prior work has shown a trade-off between efficiency and precision. In particular, the more accurate models based upon pushdown automata (PDA) are very inefficient to operate due to non-determinism in stack activity. In this paper, we present techniques for determinizing PDA models. We first provide a formal analysis framework of PDA models and introduce the concepts of determinism and stack-determinism. We then present the VP-Static model, which achieves determinism by extracting information about stack activity of the program, and the Dyck model, which achieves stack-determinism by transforming the program and inserting code to expose program state. Our results show that in run-time monitoring, our models slow execution of our test programs by 1% to 135%. This shows that reasonable efficiency needs not be sacrificed for model precision. We also compare the two models and discover that deterministic PDA are more efficient, although stack-deterministic PDA require less memory.