We consider an uplink power control problem with constraints on outage probability, for cellular CDMA systems where allocation decisions are made on a slow time-scale. A generalized framework to solve such problems for a wide range of fading distributions is proposed, including an extension that couples power control with a minimum outage probability multiuser receiver. The resulting algorithms are simple and iterative in nature that yield the optimal minimum sum-power solution. Deriving a general upper bound on outage probability, we map these problems to equivalent, sub-optimal and computationally efficient iterative algorithms. We give numerical results to validate the methods developed for a variety of Nakagami-m fading figures.