Many host species of avian brood parasites have evolved to recognize and reject foreign eggs and chicks in the nest. Yet, other hosts accept and care for parasitic young, despite the fitness losses associated with raising non-kin. It has been suggested that nest predation upon host nests by brood parasites could select for coevolved acceptance by hosts, even when their cognitive and motor traits allow for the successful rejection of brood parasitism. Using a modeling approach, I analyzed the conditions that favor the evolution of two predatory strategies by parasites and the acceptance of parasitism in the presence of predatory parasites. The Mafia strategy represents retaliatory parasites that punish rejecter hosts by depredating their nests. In contrast, the Farmer strategy represents farming parasites which depredate advanced stage host nests. Both predatory strategies benefit when hosts become available for future parasitism by renesting. The modeling showed that higher rates of parasitism and rejection, and lower rates of discovery of renests by Farmer parasites, favor the Mafia strategy over Farmer. Host acceptance of parasitism never yielded greater fitness payoffs over the rejection of parasitic eggs by hosts, implying that lack of host rejection in the presence of predatory brood parasites should not be taken as evidence of coevolution yielding an evolutionary equilibrium. Further experimental and empirical work should concentrate on documenting the frequency and context in which parasites discover and prey upon host nests, to better predict the conditions under which different strategies of predatory parasites are favored.