We find that the asymptotic bit-error probability (BEP), P-b, of a convolutionally coded code-division multiple-access (CDMA) system in a frequency-selective Rayleigh-fading channel depends on the length of the shortest error event path and the product of symbol distances (to be defined later) along that path. Based on this observation, we propose a new spreading scheme that maximizes the length of the shortest error event path. It is shown that the proposed scheme yields an improvement of 1.0-1.3 dB at P-b = 10(-5) over the conventional convolutionally coded CDMA system, and even a higher improvement can be achieved as the required BEP is decreased.