Storage integrity is essential to systems and applications that use untrusted storage (e.g., public clouds, end-user devices). However, known methods for achieving storage integrity either suffer from high (and often prohibitive) overheads or provide weak integrity guarantees. In this work, we demonstrate a hybrid approach to storage integrity that simultaneously reduces overhead while providing strong integrity guarantees. Our system, partially asynchronous integrity checking (PAC), allows disk write commitments to be deferred while still providing guarantees around read integrity. PAC delivers a 5.5 × throughput and latency improvement over the state of the art, and 85% of the throughput achieved by non-integrity-assuring approaches. In this way, we show that untrusted storage can be used for integrity-critical workloads without meaningfully sacrificing performance.