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We propose a method to count and estimate the mixing directions in an underdetermined multichannel mixture. The approach is based on the hypothesis that in the neighbourhood of some time-frequency points, only one source essentially contributes to the mixture: such time-frequency points can provide robust local estimates of the corresponding source direction. At the core of our contribution is a statistical model to exploit a local confidence measure which detects the timefrequency regions where such robust information is available. A clustering algorithm called DEMIX is proposed to merge the information from all time-frequency regions according to their confidence level. So as to estimate the delays of anechoic mixtures and overcome the intrinsic ambiguities of phase unwrapping as met with DUET, we propose a technique similar to GCC-PHAT which is able to estimate delays that can largely exceed one sample. We propose an extensive experimental study which shows that the resulting method is more robust in conditions where all DUET-like comparable methods fail, that is in particular: a) when time-delays largely exceed one sample; b) when the source directions are very close.