The unmanageably large size of reference traces has spurred the development of sophisticated trace reduction techniques. In this paper we present two new algorithms for trace re-duction — Safely Allowed Drop (SAD) and Optimal LRU Reduction (OLR). Both achieve high reduction factors and guarantee exact simulations for common replacement poli-cies and for memories larger than a user-defined threshold. In particular, simulation on OLR-reduced traces is accu-rate for the LRU replacement algorithm, while simulation on SAD-reduced traces is accurate for the LRU and OPT algorithms. OLR also satisfies an optimality property: for a given trace and memory size it produces the shortest pos-sible trace that has the same LRU behavior as the original for...