The current paper proposes fast distributed constrained power control (FDCPC) with a non stationary relaxation factor as the next power update for CDMA cellular power control systems. A review is also given of unconstrained control algorithms: distributed power control (DPC), unconstrained second order power control (USOPC), and DPC with a stationary relaxation factor (DPCSRF) To improve the performance of outage probability convergence, DCPC with a non stationary relaxation factor (FDCPC) is proposed. Under constrained conditions, the convergence rate of FDCPC is shown to outperform that of DCPC and constrained second order power control(CSOPC).