Previous treatments of the population biology of eradication have assumed that eradication can only be achieved via 100% removal of the alien population. However, this assumption appears to be incorrect because stochastic dynamics and the Allee effect typically contribute to the extinction of very low-density populations. We explore a model that incorporates Allee dynamics and stochasticity to observe how these two processes contribute to the extinction of isolated populations following eradication treatments of varying strength (percentage mortality). As a case study, we used historical data on the dynamics of isolated gypsy moth, Lymantria dispar, populations to fit parameters to this model. The parameterized model was then used in simulations that evaluated the efficacy of various eradication strategies. The results indicated that eradication of isolated gypsy moth populations could be easily achieved following a treatment of >80% mortality as long as populations were relatively low (indicated by <100 males captured in pheromone traps).