Mixed linear model (MLM) methods have proven useful in controlling for population structure and relatedness within genome-wide association studies. However, MLM-based methods can be computationally challenging for large datasets. We report a compression approach, called 'compressed MLM', that decreases the effective sample size of such datasets by clustering individuals into groups. We also present a complementary approach, 'population parameters previously determined' (P3D), that eliminates the need to re-compute variance components. We applied these two methods both independently and combined in selected genetic association datasets from human, dog and maize. The joint implementation of these two methods markedly reduced computing time and either maintained or improved statistical power. We used simulations to demonstrate the usefulness in controlling for substructure in genetic association datasets for a range of species and genetic architectures. We have made these methods available within an implementation of the software program TASSEL. © 2010 Nature America, Inc. All rights reserved.