Introduced mammalian predators are responsible for the decline and extinction of many native species, with rats (genus Rattus) being among the most widespread and damaging invaders worldwide. In a naturally fragmented landscape, we demonstrate the multi-year effectiveness of snap traps in the removal of Rattus rattus and Rattus exulans from lava-surrounded forest fragments ranging in size from <0.1 to >10 ha. Relative to other studies, we observed low levels of fragment recolonization. Larger rats were the first to be trapped, with the average size of trapped rats decreasing over time. Rat removal led to distinct shifts in the foraging height and location of mongooses and mice, emphasizing the need to focus control efforts on multiple invasive species at once. Furthermore, because of a specially designed trap casing, we observed low non-target capture rates, suggesting that on Hawai‘i and similar islands lacking native rodents the risk of killing non-target species in snap traps may be lower than the application of rodenticides, which have the potential to contaminate food webs. These efforts demonstrate that targeted snap-trapping is an effective removal method for invasive rats in fragmented habitats and that, where used, monitoring of recolonization should be included as part of a comprehensive biodiversity management strategy.