This paper considers an asynchronous direct-sequence code division multiple access (DS-CDMA) communication system over an AWGN channel. We are interested in estimating the propagation delay from the different users to the receiver. The Cram'er-Rao bound for such an estimator is derived and compared with the measured variance of three algorithms. The performance of the classical correlation-based estimator is demonstrated to be quite good in a noise-limited scenario. However, in a near-far situation, i.e., when the multiple access interference becomes dominant, the performance of the classical method is severely degraded. We therefore propose two new algorithms which are shown to be near-far resistant.