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Abstract Precipitation is one of the most difficult variables to estimate using large-scale predictors. Over South America (SA), this task is even more challenging, given the complex topography of the Andes. Empirical–statistical downscaling (ESD) models can be used for this purpose, but such models, applicable for all of SA, have not yet been developed. To address this issue, we construct an ESD model using multiple-linear-regression techniques for the period 1982–2016 that is based on large-scale circulation indices representing tropical Pacific Ocean, Atlantic Ocean, and South American climate variability, to estimate austral summer [December–February (DJF)] precipitation over SA. Statistical analyses show that the ESD model can reproduce observed precipitation anomalies over the tropical Andes (Ecuador, Colombia, Peru, and Bolivia), the eastern equatorial Amazon basin, and the central part of the western Argentinian Andes. On a smaller scale, the ESD model also shows good results over the Western Cordillera of the Peruvian Andes. The ESD model reproduces anomalously dry conditions over the eastern equatorial Amazon and the wet conditions over southeastern South America (SESA) during the three extreme El Niños: 1982/83, 1997/98, and 2015/16. However, it overestimates the observed intensities over SESA. For the central Peruvian Andes as a case study, results further show that the ESD model can correctly reproduce DJF precipitation anomalies over the entire Mantaro basin during the three extreme El Niño episodes. Moreover, multiple experiments with varying predictor combinations of the ESD model corroborate the hypothesis that the interaction between the South Atlantic convergence zone and the equatorial Atlantic Ocean provoked the Amazon drought in 2015/16.