In wireless communication systems, mobile users adapt to a time varying radio channel by regulating transmitter powers. This power control is intended to provide each user an acceptable connection, as measured by a carrier to interference ratio (CIR), by eliminating unnecessary interference. It is important that a power control algorithm can converge quickly to a fixed point at which either all users have acceptable connections or an infeasibility can be detected. In this work, we show that an iterative power control and base station assignment algorithm based on CIR measurements converges to a unique fixed point at a geometric rate. This conclusion is shown to hold even if some or all of the users are subject to maximum power constraints. The rate of convergence is evaluated by simulation of a one dimensional CDMA system.