Invasive species management involves complex and multidimensional challenges. There is considerable uncertainty regarding how to identify management strategies that will achieve invasive species control to enhance biodiversity, local economies and human well‐being. Invasive species management on inhabited islands is especially challenging, often due to perceived socio‐political risks and unexpected technical difficulties. Failing to incorporate local knowledge and local perspectives in the early stages of planning can compromise the ability of decision makers to achieve long‐lasting conservation outcomes. Hence, engaging the community and accounting for stakeholder perceptions are essential for invasive species management, yet, these processes are often overlooked as they can be perceived as too difficult to implement, too costly and/or too slow for management timeframes. To address this gap, we present an application of invasive species management based on structured decision‐making, and INFFER—a cost‐benefit analysis tool—on Minjerribah‐North Stradbroke Island (Australia). We assessed the cost‐effectiveness of six management scenarios, co‐developed with local land managers and community groups, aimed at preserving the environmental and cultural significance of the island by eradicating European red foxes (Vulpes vulpes) and feral cats (Felis catus). Information was collected in a survey that elicited local stakeholders' perspectives regarding the significance of the Island, their perception of the benefits of the proposed management scenarios, funding requirements, technical feasibility of implementation and socio‐political risk. We found that low budgets achieve less cost‐effective results than higher budgets. The best strategy focussed on controlling the European red foxes on Minjerribah. However, our results also highlight the need for more research on feral cat management. This work demonstrates how to use a structured decision support tool, such as INFFER, to assess contesting management strategies. Using appropriate decision support tools is particularly important when stakeholders' perceptions regarding management outcomes are heterogeneous and uncertain.