The genes responsible for local adaptation are likely to have more genetic differentiation among populations than do neutral genes. In principle, a good clue that a gene is affected by evolution to local conditions is that it has a higher Fst than the rest of the genome. However, testing this statistically is challenging, because some population samples are not evolutionarily independent of other samples. Typical Fst outlier approaches have high false positive rates. We introduce a new method of Fst outlier analysis–called LookWell– that adjusts for non-independent sampling. We show through simulation that LookWell gives fewer false positives and much more reliable inference.