Eradication has been achieved for many vertebrate pest control programs, primarily on small, isolated islands, but has never been considered a practical goal for invasive sea lampreys in the Laurentian Great Lakes. Our objective was to examine evidence relevant to the feasibility of setting eradication as a management goal for Great Lakes sea lampreys. Bomford and O'Brien (1995) listed six conditions for successful eradication of a vertebrate pest; here we examine evidence that these conditions are likely to be met for Great Lakes sea lampreys, with a focus on the first condition: that removal of the pest through control can exceed their rate of replenishment. We analyzed two data sets – one empirical and one synthetic – to estimate stock-recruitment relationships and calculate the exploitation rate necessary for extinction. The empirical data set included the effect of existing lampricide control and suggested an exploitation rate of 59%, in addition to lampricide control, would be sufficient for eventual eradication. The synthetic data set, derived from a simulation of stream-level recruitment dynamics in the absence of lampricide control, suggested that an overall exploitation rate of 90% would be sufficient. We suggest that both of these targets could be achieved. Meeting the other conditions will depend on the scale of the eradication effort, and on development of an exploitation strategy, such as genetic biocontrol, that can target sea lampreys in presently invulnerable habitats. Overall, we concluded that eradication of sea lampreys from the Great Lakes should not be dismissed as a prospective goal.