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Greybox fuzzing and mutation testing are two popular but mostly independent fields of software testing research that have so far had limited overlap. Greybox fuzzing, generally geared towards searching for new bugs, predominantly uses code coverage for selecting inputs to save. Mutation testing is primarily used as a stronger alternative to code coverage in assessing the quality of regression tests; the idea is to evaluate tests for their ability to identify artificially injected faults in the target program. But what if we wanted to use greybox fuzzing to synthesize high-quality regression tests? In this paper, we develop and evaluate Mu2, a Java-based framework for incorporating mutation analysis in the greybox fuzzing loop, with the goal of producing a test-input corpus with a high mutation score. Mu2 makes use of a differential oracle for identifying inputs that exercise interesting program behavior without causing crashes. This paper describes several dynamic optimizations implemented in Mu2 to overcome the high cost of performing mutation analysis with every fuzzer-generated input. These optimizations introduce trade-offs in fuzzing throughput and mutation killing ability, which we evaluate empirically on five real-world Java benchmarks. Overall, variants of Mu2 are able to synthesize test-input corpora with a higher mutation score than state-of-the-art Java fuzzer Zest.