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Trace files record the execution behavior of programs for future analysis. Unfortunately, nontrivial program traces tend to be very large and have to be compressed. While good compression schemes exist for traces that capture only the PCs of the executed instructions, these schemes can be ineffective on extended traces that include important additional information such as register values or effective addresses. Our novel, value-prediction-based approach compresses extended traces up to 22.8 times better and about two and a half times as well on average. In addition to the higher compression rate, our lossless single-pass algorithm has a fixed memory requirement and compresses traces faster than other algorithms. It achieves compression rates of up to 6170. We describe the design of our compression method and illustrate how value predictors can be used to effectively compress extended program traces.