Islands are important reservoirs of endemic and threatened species, but anthropogenic influences have impacted their biotas. Australia has over 8000 islands, both continental and oceanic, but because of considerably increased traffic, both tourist and commercial, many of these islands have been and are subject to increased threats from invasive species. The invasive Black Rat Rattus rattus is of particular concern as it can negatively impact mammal, bird, reptile, invertebrate and plant populations. Barrow Island, in northwest Western Australia, is an island requiring particular protection from Black Rats as it is a Class A nature reserve with many unique and threatened taxa that is subject to major disturbances from activities associated with oil extraction and a large liquefied natural gas processing plant. Strict quarantine is currently imposed on all materials and persons being sent to the island and there is an intense on-island surveillance programme. So far the protocols used have prevented Black Rats establishing on this island, but such a level of biosecurity is clearly impossible for all islands. In this paper we discuss the effectiveness of quarantine inspections and surveillance together and alone in protecting high-risk, high-value Australian islands against introduced rodents and we document eradication costs for other islands. World-wide, it has only been possible so far to eradicate rats from relatively small islands, mostly with no non-target indigenous mammals and larger islands only where there are no non-target indigenous mammals. Models based largely on economic considerations have suggested it is more cost effective to use surveillance alone without quarantine for Black Rats on Barrow Island and that if rats become widespread (an estimated 4% risk), it may be more cost effective not to attempt eradication. Such models provide useful guidance for managers where biodiversity values are relatively low or where there are no non-target species, but for Barrow island we argue for continuation of quarantine as well as surveillance and an increased level of quarantine controls at the point of departure on all people, vessels and aircraft visiting other vulnerable Australian islands.