When working with large sets of partial-order event data, typically collected by monitoring a distributed application, it is often desirable to search for specific patterns of events within this data. When performing such a search, we must be able to identify temporal relationships between complex sets of events. Searching for hierarchically-specified event patterns requires that a convex-closure algorithm be applied to the partial matches at each stage in the computation and the performance of such a closure algorithm can strongly influence the overall speed of pattern matching. In this paper, we propose improvements to an existing closure algorithm that significantly improve its efficiency, and also briefly discuss other possible approaches for improving performance.