Recent empirical evidence demonstrates that certain small mammals suppress breeding in response to strong predation pressure, the interpretation being that non–breeding individuals have a better chance of avoiding predation than those in a reproductive state. A separate strand of recent research has sought to explain empirical observations of cycling in small mammal (especially vole) populations of Fennoscandia as being due to their interaction with predator populations. Predator–induced breeding suppression (PIBS) is likely to have an effect on these predator–prey dynamics, and here we present a model designed to investigate this effect. We find that a strong enough level of PIBS acts to stabilize predator–prey cycles, and that weaker levels reduce the amplitude and increase the frequency of existing oscillations. These effects are explained in terms of the intrinsic mechanism driving the predator–prey cycles. We do not find circumstances where PIBS acts to destabilize an intrinsically stable interaction. We identify the features of breeding suppression that have the strongest effect on dynamic stability (e.g. quick recovery to breeding condition as predation pressure reduces), and hence pinpoint areas where future empirical research is required.