This paper introduces a novel heuristic algorithm for N-user detection in synchronous CDMA multiple access networks. In such systems, the performance of the conventional single-user detection technique (i.e. a rake receiver compounded by a set of matched filters) is clearly bounded by the well-known Multiple Access Interference (MAI). To avoid this limitation, the optimum Maximum Likelihood (ML) detection scheme seeks the best solution by performing an exhaustive search over the entire set of N-dimensional information vectors, which entails a computational complexity exponentially increasing with the number of nodes N. The heuristic procedure presented in this manuscript provides a set of near-optimum candidate vectors at a dramatically lower computational complexity. Intensive computer simulations show that our heuristic proposal outperforms the conventional single-user rake receiver, while getting close to the optimum albeit complex ML detector.