Once established, invasive species can rapidly and irreversibly alter ecosystems and degrade the value of ecosystem services. Optimal control of an exotic pest solves for a trajectory of removals that minimizes the present value of removal costs and residual damages from the remaining pest population. The shrubby tree, Miconia calvescens, is used to illustrate dynamic policy options for a forest invader. Potential damages to Hawaii's forest ecosystems are related to decreased aquifer recharge, biodiversity, and other ecosystem values. We find that population reduction is the optimal management policy for the islands of Oahu, Maui, and Hawaii. On the island of Kauai, where tree density is lower and search costs higher, optimal policy calls for deferring removal expenditures until the steady state population is reached.