Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we introduce nested lattice codes into vector perturbation systems, resulting in a strategy which we deem matrix perturbation. We propose design criteria for the nested lattice codes, and show empirically that lattices satisfying these design criteria can improve the performance of vector perturbation systems. The resulting design criteria are the same as those recently proposed for the Compute-and-Forward protocol.