Fuzzing is a popular software testing method that discovers bugs by massively feeding target applications with automatically generated inputs. Many state-of-the-art fuzzers use branch coverage as a feedback metric to guide the fuzzing process. The fuzzer retains inputs for further mutation only if branch coverage is increased. However, branch coverage only provides a shallow sampling of program behaviors and hence may discard interesting inputs to mutate. This work aims to take advantage of the large body of research in defining finer-grained code coverage metrics (such as control-flow, data-flow, or mutation coverage) and to evaluate how fuzzing performance is impacted when using these metrics to select interesting inputs for mutation. We propose to make branch coverage-based fuzzers support most fine-grained coverage metrics out of the box (i.e., without changing fuzzer internals). We achieve this by making the test objectives defined by these metrics (such as conditions to activate or mutants to kill) explicit as new branches in the target program. Fuzzing such a modified target is then equivalent to fuzzing the original target, but the fuzzer will also retain inputs covering the additional metric objectives for mutation. In addition, all the fuzzer mechanisms to penetrate hard-to-cover branches will help in covering the additional metric objectives. We use this approach to evaluate the impact of supporting two fine-grained coverage metrics (multiple condition coverage and weak mutation) over the performance of two state-of-the-art fuzzers (AFL++ and QSYM) with the standard LAVA-M and MAGMA benchmarks. This evaluation suggests that our mechanism for runtime fuzzer guidance, where the fuzzed code is instrumented with additional branches, is effective and could be leveraged to encode guidance from human users or static analyzers. Our results also show that the impact of fine-grained metrics over fuzzing performance is hard to predict before fuzzing and most of the time either neutral or negative. As a consequence, we do not recommend using them to guide fuzzers, except maybe in some possibly favorable circumstances yet to be investigated, like for limited parts of the code or to complement classical fuzzing campaigns.