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A major challenge in the operation of wireless communication systems is the effective use of radio resources to promote the quality and efficiency of the system. One such component is the power control in the mobile terminals, which is a measure of energy efficiency. Controlling the power at each wireless user not only increases the operating life of the battery, but also increases the overall system capacity by reducing the interference at each user. Game theory, a powerful tool in modelling interaction between self interested users and predicting their choice of strategies was recently used for power control in wireless data systems. Many power control algorithms have been proposed in the past decade. In this paper, we study these algorithms, present a suite of distributed power control algorithms, implement them and compare to a game theoretic algorithm. Here the concept of constraining the SIR of each user is introduced to increase the rate of convergence of these algorithms. It is also seen that the utilities increase as a result of constraining the SIR in some algorithms. We present simulation results which illustrate the utilities obtained by these algorithms, and their convergence to specified quality of service (QoS). Further, we compare the results obtained by these algorithms with the power control based on game theory.