Invasive species surveillance has typically been targeted to where the species is most likely to occur. However, spatially varying environmental characteristics and land uses may affect more than just the probability of occurrence. Biodiversity or economic value, and the ease of detection and control are also likely to vary. We incorporate these factors into a detection and treatment model of a low-density invader to determine the surveillance strategy that minimizes expected management costs. Sites with a high probability of invader occurrence and great benefits associated with detection warrant intensive surveillance; however, the optimum investment is a nonlinear function of these factors. Environments where the invader is relatively easy to detect are prioritized for surveillance, although only a moderate investment is necessary to ensure a high probability of detection. Intensive surveillance effort may be allocated to other sites if the probability of occurrence, budget and/or expected benefits is sufficiently high.