A debate is emerging over the extent to which privatization of fishery resources is socially desirable. The "pessimists" argue that there are strict limits to socially optimal privatization of such resources. The "optimists" maintain that there are no effective limits to privatization and that the decades old fear that privatization could, in some cases, lead to resource extinction are of theoretical interest only. We argue here that these fears are, regrettably, not baseless and that there are definite limits to socially desirable privatization. We discuss means by which such limits could be identified on a fishery-by-fishery basis.