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This paper describes a least absolute bound approach as a way to solve the ICA problems proposed in the 2006 MSLP competition. The least absolute bound is an ICA contrast closely related to the support width measure, which has been already studied for the blind extraction of bounded sources. By comparison, the least absolute bound applies to a broader class of sources, including those that are bounded on a single side only. This precisely corresponds to the sources involved in the competition. Practically, the minimization of the least absolute bound relies on a specific deflation algorithm with a loose orthogonality constraint. This allows solving large-scale problems without accumulating errors.