A potentially serious disadvantage of association mapping is the fact that marker-trait associations may arise from confounding population structure as well as from linkage to causative polymorphisms. Using genome-wide marker data, we have previously demonstrated that the problem can be severe in a global sample of 95 Arabidopsis thaliana accessions, and that established methods for controlling for population structure are generally insufficient. Here, we use the same sample together with a number of flowering-related phenotypes and data-perturbation simulations to evaluate a wider range of methods for controlling for population structure. We find that, in terms of reducing the false-positive rate while maintaining statistical power, a recently introduced mixed-model approach that takes genome-wide differences in relatedness into account via estimated pairwise kinship coefficients generally performs best. By combining the association results with results from linkage mapping in F2 crosses, we identify one previously known true positive and several promising new associations, but also demonstrate the existence of both false positives and false negatives. Our results illustrate the potential of genome-wide association scans as a tool for dissecting the genetics of natural variation, while at the same time highlighting the pitfalls. The importance of study design is clear; our study is severely under-powered both in terms of sample size and marker density. Our results also provide a striking demonstration of confounding by population structure. While statistical methods can be used to ameliorate this problem, they cannot always be effective and are certainly not a substitute for independent evidence, such as that obtained via crosses or transgenic experiments. Ultimately, association mapping is a powerful tool for identifying a list of candidates that is short enough to permit further genetic study.