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Power loss is one of the major drawbacks in multiple input multiple output Tomlinson Harashima precoding (MIMO-THP) schemes. In this work we explore the potential of alleviating this by optimizing the interference to be canceled. Since both the desired and interfering signals originate from the base station (BS) of the downlink system, the resulting interference can be influenced to reduce the transmission power required to cancel it, without altering the information content of the downlink message. The aim is to bring the interference closer to the replica of the desired symbol in the modulo-extended constellation. By doing so, the quantized distance between the useful signal and interference is reduced and therefore the power required to pre-subtract interference is decreased. The presented analysis and results show a considerable transmit power reduction with the proposed technique compared to conventional MIMO-THP for both zero forcing (ZF) and minimum mean squared error (MMSE) approaches.