We consider the design of soft decision functions for each stage of multistage detection for coherent demodulation in an asynchronous code-division multiple-access(CDMA) system. In particular, the sigmoid function, which is shown to be optimal under the mean square error(MSE) criterion, andmultilevel quantizers that best approximate the sigmoid function are derived. At each stage of multistage detection, the parameters of these decision functions are adjusted depending on estimated input statistics. Computer simulation results demonstrate that multistage detectors employing these soft decision functions perform considerably better than those with hard decision.