A sustainable management of global freshwater resources requires reliable estimates of the water demanded by irrigated agriculture. This has been attempted by the Food and Agriculture Organization (FAO) through country surveys and censuses, or through Global Models, which compute irrigation water withdrawals with sub-models on crop types and calendars, evapotranspiration, irrigation efficiencies, weather data and irrigated areas, among others. Here we demonstrate that these strategies err on the side of excess complexity, as the values reported by FAO and outputted by Global Models are largely conditioned by irrigated areas and their uncertainty. Modelling irrigation water withdrawals as a function of irrigated areas yields almost the same results in a much parsimonious way, while permitting the exploration of all model uncertainties. Our work offers a robust and more transparent approach to estimate one of the most important indicators guiding our policies on water security worldwide.