Compared to linear precoding, Tomlinson-Harashima precoding (THP) requires less transmit power to eliminate the spatial interference in a multi-user downlink scenario involving a multi-antenna transmitter and geographically separated receivers. However, THP gives rise to certain performance losses, referred to as modulo loss and power loss. Based on the observation that part of the users can omit the modulo operation at the receiver during an entire frame, we present an alternative detector, which reduces the modulo loss compared to the conventional detector. In addition, this contribution compares several existing and novel algorithms for selecting the user ordering and the rotation of the constellations at the transmitter, to increase the SNR at the detector and decrease the modulo loss for the alternative detector. Compared to the better of linear precoding and THP with conventional detector, the optimized alternative detector achieves significant gains (up to about 4 dB) for terrestrial wireless communication, whereas smaller gains (up to about 1 dB) are obtained for multi-beam satellite communication.