Groundwater on islands occurs in the form of freshwater lenses that serve as an important water resource for local inhabitants. These lenses are highly vulnerable to salinization due to natural recharge variations and groundwater abstraction. Determining the sustainable yield from freshwater lenses is challenging because the lens response during drought periods and the long-term effects of pumping are both difficult to predict. The exceptionally detailed and long data record for Bonriki Island of the Tarawa atoll (Kiribati) made it possible to develop a three-dimensional variable-density model of the island. Field data and modelling results highlight the strong control of rainfall variability and pumping on the temporal dynamics of the freshwater lens. The model reproduces the salinity observations in both monitoring and pumping wells reasonably well, and provides a rare example of physically based island simulation based on an extensive data set. It enables the analysis of freshwater volume and fluxes of submarine groundwater discharge, which is impossible based on the field observations alone. Under natural as well as abstraction conditions, submarine groundwater discharge responds rapidly and almost proportionally to recharge. Theoretical model scenarios with scaled abstraction rates show that lens contraction caused by pumping is a nearly linear function of the total pumped volume, whereby the abstraction rate and the timing of depletion are approximately inversely proportional. Modelling indicates that when monthly recharge inputs fall below around 2500 m3/d (i.e., a flux of 1.7 mm/d) plus the abstraction rate, the lens tends to contract. Thus, despite the highly distributed and extensive abstraction network on Bonriki Island, a significant amount of recharge is eventually lost to submarine groundwater discharge. The long-term freshwater storage trend indicates that Bonriki Island's lens is still contracting after 27.5 years of pumping, and lens thinning is threatening to impact the water supply salinity. This means that even permeable, small islands like Bonriki may take at least two decades to realise new equilibrium conditions that reflect pumping stresses, which is an important consideration in assessing the sustainable yield of small islands, in particular those less resilient to pumping than Bonriki.