The paper introduces a novel approach called "compressed MLM" to address the computational challenges associated with mixed linear model (MLM) methods in genome-wide association studies (GWAS). Compressed MLM reduces the effective sample size by clustering individuals into groups based on kinship, thereby decreasing the computational burden. Additionally, the "population parameters previously determined" (P3D) method eliminates the need for re-computing variance components, further enhancing efficiency. These methods were applied to human, dog, and maize datasets, demonstrating significant reductions in computing time while maintaining or improving statistical power. The authors also conducted simulations to validate the methods' effectiveness in controlling for substructure in various genetic architectures. The methods are implemented within the TASSEL software program, making them accessible for practical use in GWAS studies.The paper introduces a novel approach called "compressed MLM" to address the computational challenges associated with mixed linear model (MLM) methods in genome-wide association studies (GWAS). Compressed MLM reduces the effective sample size by clustering individuals into groups based on kinship, thereby decreasing the computational burden. Additionally, the "population parameters previously determined" (P3D) method eliminates the need for re-computing variance components, further enhancing efficiency. These methods were applied to human, dog, and maize datasets, demonstrating significant reductions in computing time while maintaining or improving statistical power. The authors also conducted simulations to validate the methods' effectiveness in controlling for substructure in various genetic architectures. The methods are implemented within the TASSEL software program, making them accessible for practical use in GWAS studies.