The prohibitive -exponential in the number of users- computational complexity of the maximum likelihood (ML) multiuser detector for direct-sequence code-division-multiple-access (DS/CDMA) communications has fueled an extensive research effort for the development of low complexity multiuser detection alternatives. Notable examples are the zero-forcing (``decorrelating'') and minimum-mean-square-error (MMSE) linear filter receivers. In this paper, we show that we can efficiently and effectively approach the error rate performance of the optimum multiuser detector as follows. We utilize a multiuser zero-forcing or MMSE filter as a pre-processor whose output magnitude provides a reliability measure for each user bit decision. An ordered reliability-based error search sequence of length linear to the number of users returns the most likely user bit vector among all visited options. Numerical and simulation studies for moderately loaded systems that permit the exact implementation of the optimum detector indicate that the error rate performance of the optimum and the proposed detector are nearly indistinguishable. Similar studies for higher user loads (that prohibit comparisons with the optimum detector) demonstrate error rate performance gains of orders of magnitude in comparison with straight decorrelating or MMSE multiuser detection.