In this paper, we address the problem of optimal power control in the uplink of a single cell of a multiuser interference limited wireless data network with Rayleigh fading. We propose a frame outage-based utility function that is optimized for each user. We consider two optimization problems: (1) Maximizing the minimum utility and (2) minimizing the total transmitted power subject to each user meeting their minimum utility targets. We propose simple iterative algorithms to solve these optimization problems which are seen to converge rapidly to the optimal solutions. Some numerical studies are carried out to illustrate the performance of these algorithms, demonstrating that one can achieve large utility values by spending a fairly small amount of transmit powers provided one can employ an appropriate multiuser detector at the receiver to guarantee a substantial processing gain. This allows data communication to take place with a low probability of frame outage even over rapidly fading Rayleigh channels. The power control algorithm needs to update at a much slower rate than the rate of fast channel fading, thus making it easy to implement in practice.