Top predators can suppress mesopredators by killing them, competing for resources and instilling fear, but it is unclear how suppression of mesopredators varies with the distribution and abundance of top predators at large spatial scales and among different ecological contexts. We suggest that suppression of mesopredators will be strongest where top predators occur at high densities over large areas. These conditions are more likely to occur in the core than on the margins of top predator ranges. We propose the Enemy Constraint Hypothesis, which predicts weakened top-down effects on mesopredators towards the edge of top predators’ ranges. Using bounty data from North America, Europe and Australia we show that the effects of top predators on mesopredators increase from the margin towards the core of their ranges, as predicted. Continuing global contraction of top predator ranges could promote further release of mesopredator populations, altering ecosystem structure and contributing to biodiversity loss.