Lazarus species, species that were thought to be extinct until found again, are of considerable public interest and attract major media coverage as they offer a glimmer of hope in a generally glum conservation world. This publicity could potentially generate financial and political support to prevent the species from becoming 'extinct' once again. However, it can also back-fire when publicity creates threats that were previously absent. In 2013, evidence that the Sumatran rhinoceros Dicerorhinus sumatrensis still existed in Kalimantan, the Indonesian part of the island of Borneo, made global headlines. The species was thought to have been extinct there for over a quarter of a century. The threat of poaching for its horn, however, remains as strong as ever. We question the decision to publicise this rediscovery. We argue that in the decades the species was thought to be extirpated, the population in Kalimantan could persist precisely because of the lack of attention. Interviews with hunters suggests that without information on the presence of rhinos, the perceived financial benefits of hunting down widely dispersed rhinos no longer justified the actual costs. The "publicize-and-protect" strategy now envisaged following the widely announced rediscovery of rhinos in Kalimantan requires immediate major conservation intervention, which, given the track record of conservation in Indonesia, is unlikely to be effective. We suggest that a secrecy-based strategy for Kalimantan's rhinos would have had lower risks and potentially higher long-term returns for conservation. The trade-offs facing organizations with the exciting prospect of a Lazarus species is one between the costs and benefits of publicity. Costs and benefits change over time but may not do so at the same rate, and publicity can change these rates significantly. When, without publicity, costs are expected to remain relatively constant over time, or when publicity increases the risk significantly relatively to benefits, secrecy-based strategies should be favoured to develop ways that maximize the likelihood of benefits exceeding costs. For Kalimantan's rhinos the choice to publicize-and-protect has been made, closing the door for a strategy based on secrecy, and making effective conservation solutions now all the more urgent.