In this paper, we propose an efficient superposition coding multiplexing(SCM) method based on power allocation in descending order for fading broadcast channels in which per-user minimum and maximum rate constraints are considered in order to maximize the transmission effectiveness. It consists of three steps as follows. In the first step, a user group is selected to maximize the number of users with whom a transmitter can communicate instantaneously. In the second step, per-user power allocation for each user is done in descending order of transmit power by determining a maximum allowable interference power from all subsequent interfering users in order to guarantee its corresponding minimum rate, and then a residual power is calculated. The final step is performed if some power remains even after the second step. In this step, additional power allocation is performed up to the maximum transmit power to provide the maximum rate to the corresponding user, again in ascending order, starting from the last user in descending order. But, this method does not require power reallocation to subsequent users because tentative power allocation in the second step has been performed in descending order to guarantee the minimum rate for each user, taking into account the maximum allowable interference power from all the subsequent users. Therefore, the proposed method gets more efficient in term of computational complexity when per-user minimum as well as maximum rate constraints exist, especially as the number of users increases.