Fast closed-loop-power-control (CLPC) plays a key role in direct-sequence (DS) code division multiple access (CDMA) systems, aiming at achieving acceptable carrier-to-interference (C/I) ratios in all active links. Assuming a terrestrial mobile access, where the round-trip delay may be smaller than the channel time-coherence, fast CLPC can compensate for fading and reduce the error burstiness, as well. This paper provides analytical expressions for the bit error probability given: the CLPC algorithm specified in terms of loop delay and updating rate, the propagation power-delay-profile and the terminal speed. A binary PSK DS spread spectrum radio interface, with rake processing of multipath or diversity, is considered. Our link-level analysis, being conditioned to a specified average value of CII, is focused on the inverse update algorithm, which is aimed at keeping the received power at a constant level. Applications of the derived method, aimed at getting insight about CLPC performance in 3rd generation radio interfaces, is also provided and discussed.