Most mutations are deleterious and cause a reduction in population mean fitness known as the mutational load. In small populations, weakened selection against slightly-deleterious mutations results in an additional reduction in fitness: the drift load. Many studies have established that populations can evolve a reduced mutational load by evolving mutational robustness, but it is uncertain whether populations can evolve a reduced drift load. Here, using digital experimental evolution, we show that small populations do evolve reduced drift loads, that is, they evolve robustness to genetic drift, or "drift robustness". We find that, compared to genotypes from large populations, genotypes from small populations have a decreased likelihood of small-effect deleterious mutations, thus causing small-population genotypes to be drift-robust. We further show that drift robustness is not under direct selection, but instead arises because small populations preferentially adapt to drift-robust fitness peaks. These results have implications for genome evolution in organisms with small effective population sizes.