In situations where the round-trip delay between the mobile and the base stations is smaller than the correlation time of the channel, power control schemes using feedback from the base station can effectively compensate for the fast fading due to multipath. We study several closed-loop power control (CLPC) algorithms by analysis and detailed simulation. We introduce a new loglinear model for analyzing the received power correlation statistics of a CLPC scheme. The model provides analytical expressions for the temporal correlation of the power controlled channel parameterized by the update rate, loop delay, and vehicle speed. The received power correlation statistics quantify the ability of closed-loop power control to compensate for the time-varying channel. To study more complex update strategies, detailed simulations that estimate the channel bit-error performance are carried out. Simulation results are combined with coding bounds to obtain quasi-analytic estimates of the reverse link capacity in a direct-sequence code-division multiple-access (DS-CDMA) cellular system. The quasi-analytic approach quantifies the performance improvements due to effective power control in both single-cell and multicell DS-CDMA systems operating over both frequency-nonselective and frequency-selective fading channels. The effect of nonstationary base stations on the system performance is also presented.