A reparameterization of the multivariate linear mixed model in genetic evaluation to principal components is described. This yields an equivalent model with a sparser coefficient matrix in the mixed model equations and, thus, reduced computational requirements to solve them. It is especially advantageous for analyses incorporating genomic relationship information with many nonzero elements in the inverse of the relationship matrix. Moreover, the framework lends itself directly to dimension reduction and, thus, further computational savings by omitting genetic principal components with negligible eigenvalues. The potential impact on computational demands is illustrated for an application to single-step genomic evaluation of Australian sheep.