In downstream spatial multiplexing involving multicarrier modulation using a hybrid precoder, several trade-offs have to be made with respect to the hardware complexity of the analog part of the precoder, the computational complexity of the precoders, and the performance of the communication system. Here, A class of hybrid precoding algorithms with reduced computational complexity is presented, that can be used under various hardware constraints. Our numerical results demonstrate that the proposed precoders allow one to trade off complexity against performance.