Bayesian models are described that use atent variables to model covariances. These models are flexible, scale up linearly in the number of traits, and allow
separating covariance structures in different components at the trait level and at the genomic level. Multi-trait version of the BayesA (MT-BA) and Bayesian LASSO (MT-BL) are described that model heterogeneous variance and covariance over the genome, and a model that directly models multiple genomic breeding values (MT-MG), representing different genomic covariance structures. The models are demonstrated on a mouse data set to model the genomic covariances between body weight, feed intake and feed efficiency.