Internationally, invasive vertebrate species pose a significant threat to biodiversity, agricultural production and human health. To manage these species a wide range of tools, including traps, are used. In New Zealand, brushtail possums (Trichosurus vulpecula), stoats (Mustela ermine), and ship rats (Rattus rattus) are invasive and there is an ongoing demand for cost-effective non-toxic methods for controlling these pests. Recently, traps with multiple-capture capability have been developed which, because they do not require regular operator-checking, are purported to be more cost-effective than traditional single-capture traps. However, when pest populations are being maintained at low densities (as is typical of orchestrated pest management programmes) it remains uncertain if it is more cost-effective to use fewer multiple-capture traps or more single-capture traps. To address this uncertainty, we used an individual-based spatially explicit modelling approach to determine the likely maximum animal-captures per trap, given stated pest densities and defined times traps are left between checks. In the simulation, single- or multiple-capture traps were spaced according to best practice pest-control guidelines. For possums with maintenance densities set at the lowest level (i.e. 0.5/ha), 98% of all simulated possums were captured with only a single capacity trap set at each site. When possum density was increased to moderate levels of 3/ha, having a capacity of three captures per trap caught 97% of all simulated possums. Results were similar for stoats, although only two potential captures per site were sufficient to capture 99% of simulated stoats. For rats, which were simulated at their typically higher densities, even a six-capture capacity per trap site only resulted in 80% kill. Depending on target species, prevailing density and extent of immigration, the most cost-effective strategy for pest control in New Zealand might be to deploy several single-capture traps rather than investing in fewer, but more expense, multiple-capture traps.