In a biotic environment, current reproduction will affect future population sizes, but these future changes may also affect the optimality of current reproductive decisions. We investigate the dynamics of predator–prey cycles if both predators and prey respond to each other’s (and their own) population density by adjusting their breeding effort. We find that adaptive breeding strategies of predators can produce equally profound changes to the dynamics as those produced by analogous strategies of their prey. Contrary to earlier, more limited models, we find that breeding suppression can be either destabilizing (i.e., generating cycles or chaotic behavior) or stabilizing, in cases where predators, prey, or both can adopt adjustable strategies. The direction of change depends on the shape of the density dependence in the growth rates, as well as how it is affected by the breeding decisions. We discuss these findings in light of the Fennoscandian vole cycle, where antipredatory behavior of voles has been evoked to explain some properties of the cycle, and where many predators show pronounced variability in their breeding effort according to the phase of the cycle.