A radio power control strategy to achieve maximum throughput for the up-link of CDMA wireless systems with variable spreading factor is investigated. The system model includes slow and fast fading, rake receiver, and multi-access interference caused by users with heterogeneous data sources. The quality of the communication is expressed in terms of outage probability, while the throughput is defined as the sum of the users' transmit rates. The outage probability is accounted for by resorting to a lognormal approximation. A mixed integer-real optimization problem P-1, where the objective function is the throughput under outage probability constraints, is investigated. Problem P-1 is solved in two steps: firstly, we propose a modified problem P-2 to provide feasible solutions, and then the optimal solution is obtained with an efficient branch-and-bound search. Numerical results are presented and discussed to assess the validity of our approach.