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We formulate the resource assignment problem of maximizing the spectral efficiency of a wireless system subject to user satisfaction constraints in the multiservice scenario that is a challenging resource allocation problem from the system operators' point of view. We show that although this optimization problem is nonlinear, it can be converted to an integer linear program. This way, the optimal solution can be obtained by standard techniques. Due to the high computational complexity to obtain the optimal solution, we propose a fast suboptimal algorithm named Reallocation-based Assignment for Improved Spectral Efficiency and Satisfaction (RAISES). Simulation results show that our proposal achieves near-optimal performance in low and medium loads with a much lower computational complexity compared with the algorithm used to obtain the optimal solution. Therefore, the RAISES algorithm achieves a good tradeoff between performance and computational complexity.