This paper develops a model of invasive species control when the species' population size is unknown. In the face of an uncertain population size, a resource manager's species-control efforts provide two potential benefits: (1) a direct benefit of possibly reducing the population of invasive species, and (2) an indirect benefit of information acquisition (due to learning about the population size, which reduces uncertainty). We provide a methodology that takes into account both of these benefits, and show how optimal management decisions are altered in the presence of the indirect benefit of learning. We then apply this methodology to the case of controlling the Brown Treesnake (Boiga irregularis) on the island of Saipan. We find that the indirect benefit--the value of information to reduce uncertainty--is likely to be quite large.