Pacific island economies are some of the most remittance dependent in the world. Proposals to lower the costs of sending money across borders are a core recommendation of recent international studies that aim to enhance the development impact of remittances. The potential increase in remittances that recipient countries can expect from such policies depends critically on the sensitivity of remittance transfers to the costs of remitting. This paper provides the first estimates of the cost elasticity of remittances, using data from a survey of Tongan migrants in New Zealand. The costs of remitting to Tonga are high by international standards and remittances are found to have a negative cost-elasticity with respect to the fixed fee component of money transfer costs. These findings suggest that Pacific island countries can expect a more than proportionate increase in remittances from a reduction in costs.