Summary Population admixture can be a confounding factor in genetic association studies. Family-based methods (Rabinowitz and Larid, 2000, Human Heredity 50, 211–223) have been proposed in both testing and estimation settings to adjust for this confounding, especially in case-only association studies. The family-based methods rely on conditioning on the observed parental genotypes or on the minimal sufficient statistic for the genetic model under the null hypothesis. In some cases, these methods do not capture all the available information due to the conditioning strategy being too stringent. General efficient methods to adjust for population admixture that use all the available information have been proposed (Rabinowitz, 2002, Journal of the American Statistical Association 92, 742–758). However these approaches may not be easy to implement in some situations. A previously developed easy-to-compute approach adjusts for admixture by adding supplemental covariates to linear models (Yang et al., 2000, Human Heredity 50, 227–233). Here is shown that this augmenting linear model with appropriate covariates strategy can be combined with the general efficient methods in Rabinowitz (2002) to provide computationally tractable and locally efficient adjustment. After deriving the optimal covariates, the adjusted analysis can be carried out using standard statistical software packages such as SAS or R. The proposed methods enjoy a local efficiency in a neighborhood of the true model. The simulation studies show that nontrivial efficiency gains can be obtained by using information not accessible to the methods that rely on conditioning on the minimal sufficient statistics. The approaches are illustrated through an analysis of the influence of apolipoprotein E (APOE) genotype on plasma low-density lipoprotein (LDL) concentration in children.