Models were presented that describe the attraction and killing at toxic baits or traps of adult males and females of an insect pest species. These models were used to test the effects of the following factors on ease of control: female monogamy versus polygamy, attraction of only males versus both sexes, initiating mating before versus after responding to baits/traps, the ability of males to mate many times each day versus only once per day, and the existence of a time lag of several days before females can mate versus mating immediately after emergence. The models indicated that mating before trapping or the ability of males to mate many times each day will probably render this control method ineffective. The other factors tested (mating habit and specifics of attraction) had little effect on the efÞciency of trapping males as a control method. We then included age structure and a refractory period for virgin females before they can mate. The models were then made specific to Bactrocera dorsalis (Hendel) (Diptera: Tephritidae) by using parameter values derived from the literature. The results of the models imply that the attraction and killing of large numbers of males is rather ineffective to suppress populations. However, the combination of attracting both males and females can be more effective than attracting either sex alone. The increased attraction of females to methyl eugenol baits that has been observed with the declining presence of males during Male Annihilation Technique campaigns may explain the reported effectiveness against invasive Bactrocera pest species.