Imperfect scientific information regarding potential invasiveness, differences between private and public outcomes for individual decisions regarding planting, and inadequate prevention activity combine to impose costs through a change in native ecosystems susceptible to invasion by hardy, rapidly reproducing non-indigenous species. Concepts and tools from economic theory that may improve policy decisions are explored through the specific example of Miconia calvescens in Hawaii. Rapid expansion of Miconia calvescens, an ornamental tree introduced to several Pacific Islands over the last century, threatens local watersheds, endangered species, and recreational and aesthetic values in the Hawaiian and Society Islands. Potential welfare losses from the unchecked spread of Miconia in Hawaii are illustrated. Policy options investigated include accommodation of these losses, efforts at containment, or eradication. Estimates are determined through an optimal control model describing the potential expansion of the weed and its control costs and damages. Results suggest that cost-effective policies will vary with the level of invasion as well as the expected net benefits from control efforts.