We consider power control for the reverse link of a DS/CDMA system where received powers are to be controlled to achieve specified BERs for individual users, not necessarily the same. Our emphasis is to work with bit error rates (BERs), which are more readily measurable than the signal to interference ratios (SIRs), which received a lot of attention in the literature. The power control algorithm that we propose works without knowledge of the relationship between the BER and the SIR. The convergence of this algorithm is shown for a general class of expressions for the BER encountered in digital communications.