The power assignment problem is important for Multiple-Input-Multiple-Output (MIMO) systems to achieve high capacity. Although this problem is solved by well-known water filling algorithms, this does not provide an optimal solution if the system is constrained to a fixed raw bit error rate threshold and to discrete modulation orders. In this work an approximate approach, called QoS based WF, is proposed to solve the power assignment problem with such constrains. It is shown to outperform quantization of the conventional water filling solution and a well known bit loading algorithm (Chow's algorithm) used in the Digital Subscriber Lines (DSL).