Archaeologists have been using luminescence to date pottery in South America since the late 1970s, inspired by early success in northern Chile. However, luminescence dates have not been rigorously compared to independent dating methods, which this paper’s goal. First, we present a compilation of 94 paired 14C and luminescence dates from the southern Andes, which reveals discrepancies across a range of contexts and ages. Second, we compare two Bayesian models of sets of 14C and thermoluminescence (TL) dates from three ceramic styles in the Azapa Valley, Chile, and the Inca occupation of Mendoza, Argentina. We find that only the 14C models produce results that agree with expectations based on independent data. Third, we present results from a pilot study in Mendoza that dated 6 sherds with 3 luminescence methods each and closely associated 14C dates. The reasons for disagreement between methods remain unclear, but Andean sediments with low and unstable luminescence sensitivity seem to be an important factor. Even though some luminescence ages are accurate, the clear trend of inconsistent results leads us to recommend that archaeologists use 14C rather than luminescence dates to build cultural chronologies.