Accurate estimation of missing daily precipitation data remains a difficult task. A wide variety of methods exists for infilling missing values, but the percentage of gaps is one of the main factors limiting their applicability. The present study compares three techniques for filling in large amounts of missing daily precipitation data: spatio-temporal kriging (STK), multiple imputation by chained equations through predictive mean matching (PMM), and the random forest (RF) machine learning algorithm. To our knowledge, this is the first time that extreme missingness (>90%) has been considered. Different percentages of missing data and missing patterns are tested in a large dataset drawn from 112 rain gauges in the period 1975–2017. The results show that both STK and RF can handle extreme missingness, while PMM requires larger observed sample sizes. STK is the most robust method, suitable for chronological missing patterns. RF is efficient under random missing patterns. Model evaluation is usually based on performance and error measures. However, this study outlines the risk of just relying on these measures without checking for consistency. The RF algorithm overestimated daily precipitation outside the validation period in some cases due to the overdetection of rainy days under time-dependent missing patterns.