Invasive alien species pose a significant threat to biodiversity worldwide and many eradication programmes are now underway in an effort to reduce the impact they may have on native species and ecosystems. The spatial structure of such invasive species populations is likely to have important implications for designing effective control strategies. Here, a simple source–sink population model is used to address the following question: if a population of an invasive alien species is source–sink in nature, what is the best way of dividing limited resources for its control? Results from this model indicate that allocation of resources solely to the source population does not always result in the most effective control strategy. The most efficient control measure is determined by the relative strengths (net gains and losses) of the source and sink populations and, crucially, the nature of dispersal between them. We present a case study for the control of an invasive species illustrating the use of these types of model.