A logistic model of population growth is presented which describes the effects of introducing sterile individuals into a wild population regulated by density-dependent factors. It is shown that for certain levels of sterile releases two steady states exist, of which the upper state is stable and the lower state is unstable. Once a population is driven to below the lower threshold, continued releases will cause (local) extinction. The 2 steady states exist for a wide variety of density-dependent growth functions. The release of sterile males alone is less effective than the release of sterile males and sterile females but not importantly so; however, the release of sterile females alone is not a satisfactory strategy for eradication.