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A class of adaptive algorithms for DS-CDMA interference suppression is presented based on the multistage Wiener filter introduced by Goldstein and Reed (see IEEE Trans. Inform. Theory, vol. 44, no.7, 1998). Unlike the principal-components method for reduced-rank filtering this method performs well when the subspace spanned by the filter is less than the dimension of the signal subspace. We present block and recursive algorithms for estimating the filter parameters, which do not require matrix inversion or an eigen-decomposition The algorithm performance in the context of a heavily loaded DS-CDMA system is characterized via computer simulation.