We present simple models that describe the factors influencing application of the Sterile Insect Technique (SIT) alone, followed by the factors affecting the integration of the Male Annihilation Technique (MAT) and SIT simultaneously to annihilate wild males and replace them with methyl eugenol (ME)-exposed sterile males that are less responsive to the toxic MAT baits. The removal by MAT of large numbers of males to deprive females of mates is rather ineffective to suppress populations unless a proportion of females are also attracted to baits. When simultaneously implementing SIT and MAT, much less stringent requirements for the annihilation of the wild male population apply and the sterile fly release rate can be reduced to only ≈5% of that when SIT is applied alone. The main determinants of control efficiency are whether a proportion of wild females is attracted to MAT baits, whether most of the wild males respond to the MAT baits before mating, and whether a majority of ME-exposed sterile males do not respond to the baits. However, a high remating frequency in mated females, and the release of only sterile males or both sterile males and females, do not greatly affect the ease of control. We conclude that the simultaneous MAT and SIT application is synergistic and the combination appears to be an extremely powerful control strategy for tephritid fruit fly pests that are attracted to ME.