Power control is an effective technique to reduce cochannel interference and increase capacity for cellular radio systems. Optimum centralized power control can minimize the outage probability, but requires the information of all link gains in real time, which is very difficult to successfully implement for a large system; besides, the computational complexity of an optimum power control algorithm makes it impractical for real implementations. In this paper, we propose some centralized power control algorithms with reasonable computational complexity. One of the algorithms, called the SMIRA algorithm, has an outage probability that is very close to the minimum. We also study a class of distributed power control algorithms that can achieve a balanced carrier-to-interference ratio with probability one. Among the class of algorithms, we found that the one proposed in  gives the minimum outage probability.