Application of the turbo principle to multiuser decoding results in an exchange of probability distributions between two sets of constraints. Firstly, constraints imposed by the multiple-access channel, and secondly, individual constraints imposed by each users' error control code. A-posteriori probability computation for the first set of constraints is prohibitively complex for all but a small number of users. Several lower complexity approaches have been proposed in the literature. One class of methods is based on linear filtering (e.g. LMMSE). A more recent approach is to compute approximations to the posterior probabilities by marginalising over a subset of sequences (list detection). Most of the list detection methods are restricted to non-singular systems. In this paper, we introduce a transformation that permits application of standard tree-search methods to underdetermined systems. We find that the resulting tree-search based receiver outperforms existing methods.