A novel strategy for reducing the power loss in Tomlinson-Harashima precoding (THP) is explored in this paper, based on optimizing the interference to be canceled. A multiple input multiple output (MIMO) downlink transmission is considered and the proposed strategy is motivated by the fact that both the desired and interfering signals originate from the base station (BS) of the downlink system itself. The resulting interference can therefore be influenced to reduce the transmission power required to cancel it, without altering the information content of the downlink message. This optimization aims at bringing the interference closer to the replicas of the desired symbols for all users in the THP modulo-extended constellation. By doing so, the quantized distance between the useful signal and interference is reduced and therefore the power required to presubtract interference is decreased. Based on this concept, a new practical THP transmitter for multiple input multiple output systems (MIMO-THP) is designed. The effect of the interference optimization is studied by means of mathematical analysis and simulation and towards this end, the Gaussian-Modulo distribution is derived and used to describe the distribution of the modulo-precoded transmitted symbols. This is proven to provide a closer approximation of the power loss for both conventional and proposed MIMO-THP techniques, compared to the approximation based on the uniform distribution used in the literature. Theoretical and simulation results both confirm that, by optimizing the interference to be canceled, the proposed technique offers a considerable transmit power reduction compared to conventional THP while securing a slightly improved error rate performance.