There is a broad agreement that psychology is facing a replication crisis. Even some seemingly well-established findings have failed to replicate. Numerous causes of the crisis have been identified, such as underpowered studies, publication bias, imprecise theories, and inadequate statistical procedures. The replication crisis is real, but it is less clear how it should be resolved. Here we examine potential solutions by modeling a scientific community under various different replication regimes. In one regime, all findings are replicated before publication to guard against subsequent replication failures. In an alternative regime, individual studies are published and are replicated after publication, but only if they attract the community’s interest. We find that the publication of potentially non-replicable studies minimizes cost and maximizes efficiency of knowledge gain for the scientific community under a variety of assumptions. Provided it is properly managed, our findings suggest that low replicability can support robust and efficient science.