An important policy decision in managing invasive species is how to allocate resources between activities aimed at preventing the arrival of new pests - including additional arrivals of existing pests - and activities aimed at reducing the damages done by species that are already here. We develop a dynamic model for managing a generic invasive pest with an uncertain arrival date. The optimal conditions reveal that it is generally more efficient to spend a larger share of outlays for exclusion activities before a species arrives than after it is known to be here. They also show that outlays should be allocated such that the marginal costs of control measures equal the benefits from the marginal reduction of the species' population growth rate, and the marginal costs of exclusion measures equal the benefits from the marginal reduction of the rate of subsequent arrivals.