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• Tuta absoluta existence only depends on environmental characteristics. • The predator population persists in the system even when the parasitism is stronger. • Coexistence of predators and parasitoids is a better option of pest control. • If coexistence is not possible, strongest controlling population remains in system. The Tuta absoluta (Meyrick) (Lepidoptera, Gelechiidae), or tomato leafminer, is one of the most devastating pests of tomato crops in South America. The use of parasitoids and predators as biocontrol agents of this pest is an alternative to chemical insecticides and an environmentally safe strategy. However, an outcome of a three-way interspecific interaction (pest-parasitoid-predator) may bring surprises. The question is thus how a combination of enemies can contribute most effectively to reduction of the pest density. We examine this using an ordinary differential equations model. The formal and numerical analyses show that the joint use of both biological controls is the best option to decrease the tomato leafminer population, in contrast to the use of each biological control agent separately. Specifically, the numerical results show that in a scenario where the only biological control is given by the parasitoid, the introduction of the predator decreases the adult Tuta population by 28 % , reducing even more the damage caused in tomato crops compared to the use of parasitoid alone. [ABSTRACT FROM AUTHOR]