Fuzzing is the de-facto default technique to discover software flaws, randomly testing programs to discover crashing test cases. Yet, a particular scenario may only care about specific code regions (for, e.g., bug reproduction, patch or regression testing)—spurring the adoption of directed fuzzing. Given a set of pre-determined target locations, directed fuzzers drive exploration toward them through distance minimization strategies that (1) isolate the closest-reaching test cases and (2) mutate them stochastically. However, these strategies are applied onto every explored test case—irrespective of whether they ever reach the targets—stalling progress on the paths where targets are unreachable. Accelerating directed fuzzing requires prioritizing target-reachable paths. To overcome the bottleneck of wasteful exploration in directed fuzzing, we introduce tripwiring: a lightweight technique to preempt and terminate the fuzzing of paths that will never reach target locations. By constraining exploration to only the set of target-reachable program paths, tripwiring curtails directed fuzzers’ search noise—while unshackling them from the high-overhead in- strumentation and bookkeeping of distance minimization—enabling directed fuzzers to obtain up to 99× higher test case throughput. We implement tripwiring-directed fuzzing as a prototype, SieveFuzz, and evaluate it alongside the state-of-the-art directed fuzzers AFLGo, BEACON and the leading undirected fuzzer AFL++. Overall, across nine benchmarks, SieveFuzz’s tripwiring enables it to trigger bugs on an average 47% more consistently and 117% faster than AFLGo, BEACON and AFL++.