In this paper, we conduct a number of cost-benefit analyses to clarify whether the establishment of invasive species should be prevented or the damage of such species should be mitigated after introduction. We use the potential establishment of ragweed in Denmark as an empirical case. The main impact of the establishment of this invasive species is a substantial increase in the number of allergy cases, which we use as a measure of the physical damage. As valuation methods, we use both the cost-of-illness method and the benefit transfer method to quantify the total gross benefits of the two policy actions. Based on the idea of an invasion function, we identify the total and average net benefit under both prevention and mitigation. For both policy actions, the total and average net benefits are significantly positive irrespective of the valuation method used; therefore, both prevention and mitigation are beneficial policy actions. However, the total and average net benefits under mitigation are larger than the benefits under prevention, implying that the former policy action is more beneficial. Despite this result, we conclude that prevention, not mitigation, shall be used because of information externalities, altruistic preferences, possible catastrophic events and ethical considerations.