Studies on tactical deception have reported that informed subordinates can withhold information from naive dominants, but they have not directly compared species' performance. Here, we compared the performance in two withholding-of-information tasks of three monkey species differing in the strictness of their dominance hierarchy and degree of fission-fusion dynamics: spider monkeys, capuchin monkeys and long-tailed macaques. Food was hidden from the dominants' view either inside an opaque box or in a transparent box that could only be opened by knowledgeable subordinates. All species were capable of withholding information, with subjects refraining from interacting with the box when the dominant was nearby. Spider monkeys were the most efficient at retrieving food, by timing it when the dominant was far from the box. Capuchin monkeys were also quite efficient when alone at the box, but they lost much of the food when manipulating the box with the dominant nearby. The results supported our predictions based on interspecific differences in the strictness of the dominance hierarchy and the degree of fission-fusion dynamics, with the former constraining the subjects' tendency to approach the box and the latter affecting the subjects' tendency to wait for the appropriate situation to retrieve the food.