The bit error probability (BEP) of binary and quaternary PSK (BPSK and QPSK) signals over Rayleigh fading channel with imperfect carrier-phase recovery is derived. The channel is assumed to be slow and frequency-nonselective in which the received signal is constant over at least two symbol intervals. Numerical values for the average BEP are obtained by integrating the conditional BEP expression over the carrier-phase error distribution. The resultant integrands have only elementary functions, such as exponentials and algebraic power functions and can, therefore, be explicitly evaluated to any degree of accuracy. The accuracy of this approach is verified through proposing an efficient quazi-analytical simulation technique.