The capacity of cellular mobile radio systems can be increased by controlling the transmitter powers so as to balance the carrier to interference ratios at the receivers. A distributed algorithm for implementing such power control was proposed earlier for satellite systems by Meyerhoff (1974). The authors tighten the mathematical arguments and apply this scheme to cellular systems. The mobile units adjust their transmitter powers at discrete time instants. Specifically at each time instant the mobile multiplies its current power by a factor equal to a constant over its current carrier to interference ratio (CIR). So power is increased or decreased based on the value of the current CIR. After a number of such power adjustments all the mobiles converge to a common CIR. They also present numerical results which show that the above scheme has the potential to converge faster than the scheme proposed by J. Zander (see IEEE Transactions on Vehicular Technology, vol.41, no.3, August 1992) for high CIR values. >