We characterize the maximum throughput achievable for the up-link of a power-controlled WCDMA wireless system with variable spreading factor. Our system model includes multi access interference caused by users with heterogeneous data sources, and quality of service expressed in terms of outage probability. Inner loop and outer loop power control mechanisms are also explicitly taken into account. We express the system throughput as the sum of the users transmission rates, and propose a mixed integer optimization program where the objective function is the sum of the rates under outage probability constraints. Then, we solve the optimization problem proposing an efficient optimal approach based on two steps: firstly, a modified problem provides feasible solutions, and then the optimal solution is obtained with branch and bound criteria. Numerical results confirm the validity of our approach, and show how the throughput depends on the power control fluctuation, activity of the sources, and quality of service.