Population control of invasive mammal pests is an ongoing process in many conservation projects. In New Zealand, introduced wild domestic cats and mustelids have a severe impact on biodiversity, and methods to reduce and maintain predator populations to low levels have been developed involving poisoning and trapping. Such conservation efforts often run on limited funds, so ways to minimize costs while not compromising their effectiveness are constantly being sought. Here we report on a case example in a 150 km2 area in the North Island, New Zealand, where high predator numbers were reduced by 70-80% in an initial 'knockdown' trapping program, using the full set of traps available in the fixed network and frequent checks, and then maintained at low density using maintenance trapping with less frequent checking. We developed and applied a simulation model of predator captures, based on trapping data, to investigate the effect on control efficacy of varying numbers of trap sites and numbers of traps per site. Included in the simulations were captures of other, non-target, introduced mammals. Simulations indicated that there are potentially significant savings to be made, at least in the maintenance phase of a long-term predator control programme, by first reducing the number of traps in large-scale networks without dramatically reducing efficacy, and then, possibly, re-locating traps according to spatial heterogeneity in observed captures of the target species.