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We describe a generalized version of hierarchical IDEAL that can flexibly handle arbitrary chemical species at arbitrary echo times. The proposed work is fast and robust, and it has three key features: (1) multiresolution approach, which allows the method to handle images with disjoint regions, makes it less susceptible to local optima, and reduces the ambiguity of the separation; (2) direct phase estimation, which bypasses the phase wrapping issue, and (3) efficient algebraic formulation, which enables fast calculation and insensitivity to spatially varying phase across the image, from sources such as partial echo acquisition, receiver coils, motion, and flow. Representative results at 1.5 T and 3 T are presented from human ankle, wrist, and a water/oil/silicone phantom. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.