Simultaneous wireless information and power transfer can be achieved using an integrated receiver, where the incoming signal is rectified, and both the energy harvesting (EH) and the information detection (ID) operate on this rectified signal. Because phase information is lost at the input of the ID, commonly-used modulation techniques cannot be straightforwardly applied and biased M-ASK is used instead. We consider downstream communication over a Rician block-fading channel, from a multi-antenna hasestation to a number of single-antenna users. Multi-user interference is eliminated by applying zero-forcing preceding. Using a realistic rectifier model, we compare EH and ID performances of linear precoding (LP) and modified Tomlinson-Harashima preceding (THP). We add low-complexity algorithms to these precoders that optimize the user ordering and the constellation rotations. Moreover, we investigate the effect of the amplitude ratio rho(ASK) of’ the constellation on the energy-rate trade-off. Compared to the same precoders without optimization, optimizing the user ordering, rotations and rho(ASK) considerably reduces the transmit power required to achieve a harvested power of -30 dBm or an average mutual information of (log(2) M)/2. Both with and without optimizations, THP outperforms LP in terms of EH and ID, but THP exhibits much larger gains when optimizations are applied.