Association studies among admixed populations pose many challenges including confounding of genetic effects due to population substructure and heterogeneity due to different patterns of linkage disequilibrium (LD). We use simulations to investigate controlling for confounding by indicators of global ancestry and the impact of including a covariate for local ancestry. In addition, we investigate the use of an interaction term between a single-nucleotide polymorphism (SNP) and local ancestry to capture heterogeneity in SNP effects. Although adjustment for global ancestry can control for confounding, additional adjustment for local ancestry may increase power when the induced admixture LD is in the opposite direction as the LD in the ancestral population. However, if the induced LD is in the same direction, there is the potential for reduced power because of overadjustment. Furthermore, the inclusion of a SNP by local ancestry interaction term can increase power when there is substantial differential LD between ancestry populations. We examine these approaches in genome-wide data using the University of Southern California's Children's Health Study investigating asthma risk. The analysis highlights rs10519951 (P = 8.5 × 10(-7)), a SNP lacking any evidence of association from a conventional analysis (P = 0.5).