Several ways of using sterile insects for their own destruction have been suggested (Knipling 1955, 1959, 1966). With regard to releasing sterile insects into natural population, Monro (1963, 1966) suggested and obtained data to support the suggestion that adding large numbers of such insects to an environment could also contribute materially to control by causing the population to disperse because the supply of resources essential to all the insects present would become overloaded. However, a significant additional insect population suppression factor might result if necessary resources were added to the environment to permit an increase in the rate of predation. This was recently suggested by Shipp and Osborn (1966). I have also suggested in personal communications to the staff of the Entomology Research Division that an increase in the rate of parasitism or predation might be achieved by adding sterilized insects to the environment. The suggestion pertained particularly to the addition to the environment of sterile eggs within or on which parasites or predators might develop. The purpose of this paper is to support the views of Shipp and Osborn and to present the results of studies with hypothetical insect population models subjected to population suppression by releasing both sterile males and sterile egg-laying females.