The bit error rate (BER) analysis of an asynchronous direct-sequence code-division multiple-access (DS-CDMA) cellular system over Rayleigh-fading channels often results in complicated expressions even though Gaussian approximation is applied. Numerical computation of this expression is limited by the issues of complexity, efficiency and accuracy. As a result, a combined pdf approach for the forward link and a mean-method technique for the reverse link are proposed to reduce the computational complexity and increase the accuracy, significantly. The essential theory in deriving the simplified BER expressions for both links is presented. Observation on the simplified expressions shows that the computational effort for these two approaches grows only linearly with the number of interfering cells in the system regardless of the number of active mobiles in the cell. Finally, comparison with simulation shows that the results obtained are very accurate.