Out of the almost 2,000 plants that have been selected as crops, only few are fully domesticated, and many intermediates between wild plants and domesticates exist.Here we investigate the incomplete domestication of an ancient grain from the Americas, amaranth.We sequenced 121 genomes of the crop and its wild ancestors to show that grain amaranth has been selected three times independently from a single wild ancestor, but has not been fully domesticated.We demonstrate that the domestication trait seed color was independently converted in Central and South America and identify a MYB-like transcription factor gene as possible key regulator for this trait.We suggest low effective population size at the time of domestication as potential cause for a lack of adaptation of complex domestication traits.Our results show how genetic constraints influenced domestication and might have set the fate of hundreds of crops.