Invasive alien species rank among the world's greatest threats to biodiversity and cause huge economic losses. Eradication is a key management strategy for newly introduced pests, but it is frequently discarded due to the high costs. When populations become established and conflicts increase, policy-makers often resort to permanent population control. However, no cost-benefit analyses have been carried out so far to compare the two alternatives. We present the first cost-benefit analysis by comparing the permanent control campaign of coypu Myocastor coypus in Italy with the successful eradication carried out in UK in the 1980s. Data regarding the eradication came from literature, while costs and benefits of control were quantified through a national survey. In Italy, during 1995-2000, the damage amounted to € 11,631,721, control activities cost € 2,614,408, and 220,688 coypu were removed. Control campaigns did not stop the population expansion nor the increase in damage and economic losses at a national scale. However, the efficacy of local campaigns varied among different ecosystems. According to our predictions, the Italian coypu range may expand 2.5-3.3 times, and economic losses may reach € 9-12 millions/year. A comparison between the costs of the successful eradication carried out in East Anglia (€ five million over 11 years) and the permanent control campaign in Italy (€ 14 million over only six years) shows that even very costly eradications, if successful, may have a very positive cost-benefit ratio in the long term.