Most fuzzing efforts, very understandably, focus on fuzzing the program in which bugs are to be found. However, in this paper we propose that fuzzing programs “near” the System Under Test (SUT) can in fact improve the effectivness of fuzzing, even if it means less time is spent fuzzing the actual target system. In particular, we claim that fault detection and code coverage can be improved by splitting fuzzing resources between the SUT and mutants of the SUT. Spending half of a fuzzing budget fuzzing mutants, and then using the seeds generated to fuzz the SUT can allow a fuzzer to explore more behaviors than spending the entire fuzzing budget on the SUT. The approach works because fuzzing most mutants is “almost” fuzzing the SUT, but may change behavior in ways that allow a fuzzer to reach deeper program behaviors. Our preliminary results show that fuzzing mutants is trivial to implement, and provides clear, statistically significant, benefits in terms of fault detection for a non-trivial benchmark program; these benefits are robust to a variety of detailed choices as to how to make use of mutants in fuzzing. The proposed approach has two additional important advantages: first, it is fuzzer-agnostic, applicable to any corpus-based fuzzer without requiring modification of the fuzzer; second, the fuzzing of mutants, in addition to aiding fuzzing the SUT, also gives developers insight into the mutation score of a fuzzing harness, which may help guide improvements to a project’s fuzzing approach.