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Modified branch metrics are proposed for single-user Viterbi decoders in two-stage detectors for convolutionally-encoded code-division multiple-access (CDMA) systems with random spreading sequences. The modifications are based on modeling the residual multiple-access interference (RMAI) after subtractive interference cancellation as conditionally Gaussian with time-dependent variance, where the conditioning is on the time-varying user crosscorrelations. A novel estimate of the variance of the total RMAI is presented, and used in the proposed branch metrics. Significant performance gains are demonstrated over the Euclidean branch metric of the standard Viterbi decoder.