Conservation measures often result in a “wicked problem,” i.e., a complex problem with conflicting aims and no clear or straightforward resolution without severe adverse effects on one or more parties. Here we discuss a novel approach to an ongoing problem, in which actions to reduce risk to humans, involve lethal control of otherwise protected species. To protect water users, nets are often used to catch potentially dangerous sharks at popular bathing beaches, yet in Australian waters one of the targeted species, the white shark (Carcharodon carcharias) is listed as Vulnerable, while bycatch includes the Critically Endangered grey nurse shark (Carcharias taurus). Recent, highly publicised, shark attacks have triggered demands for improved bather protection, whilst welfare and conservation organisations have called for removal of lethal measures. This leaves management and policy makers with a wicked problem: removing nets to reduce impacts on threatened species may increase risk to humans; or leaving the program as it is on the premise that the benefits provided by bather protection are greater than the impact on threatened and protected species. We used multivariate analysis and generalised additive models to investigate the biological, spatial-temporal, and environmental patterns influencing catch rates of threatened and of potentially dangerous shark species in the New South Wales shark nets over two decades to April 2019. Factors influencing catches were used to develop a matrix of potential changes to reduce catch of threatened species. Our proposed solutions include replacing existing nets with alternative mitigation strategies at key beaches where catch rate of threatened species is high. This approach provides stakeholders with a hierarchy of scenarios that address both social demands and threatened species conservation and is broadly applicable to human-wildlife conflict scenarios elsewhere.