Species invasions have a range of negative effects on recipient ecosystems, and many occur at a scale and magnitude that preclude complete eradication. When complete extirpation is unlikely with available management resources, an effective strategy may be to suppress invasive populations below levels predicted to cause undesirable ecological change. We illustrate this approach by developing and testing targets for the control of invasive Indo-Pacific lionfish (Pterois volitans and P. miles) on Western Atlantic coral reefs. We first developed a size structured simulation model of predation by lionfish on native fish communities, which we used to predict threshold densities of lionfish beyond which native fish biomass should decline. We then tested our predictions by experimentally manipulating lionfish densities above or below reef-specific thresholds, and monitoring the consequences for native fish populations on 24 Bahamian patch reefs over 18 months. We found that reducing lionfish below predicted threshold densities effectively protected native fish community biomass from predation-induced declines. Reductions in density of 75- 95%, depending on the reef, were required to suppress lionfish below levels predicted to over-consume prey. On reefs where lionfish were kept threshold densities, native prey fish biomass increased by 50-70%. Gains in small (<6cm) size classes of native fishes translated into lagged increases in larger size classes over time. The biomass of larger individuals (>15cm total length), including ecologically important grazers and economically important fisheries species, had increased by 10-65% by the end of the experiment. Crucially, similar gains in prey fish biomass were realized on reefs subjected to partial and full removal of lionfish, but partial removals took 30% less time to implement. By contrast, the biomass of small native fishes declined by more than 50% on all reefs with lionfish densities exceeding reef-specific thresholds. Large inter-reef variation in the biomass of prey fishes at the outset of the study, which influences the threshold density of lionfish, means that we identify a single rule-of-thumb for guiding control efforts. However, our model provides a method for setting reef-specific targets for population control using local monitoring data. Our work is the first to demonstrate that for ongoing invasions, suppressing invaders below densitiesterms of protecting the native ecosystem on a local scale, to achieving complete eradication