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Segmentation of very high resolution remote-sensing images cannot rely only on spectral information, quite limited here for technological reasons, but must take into account also the rich textural information available. To this end, we proposed recently the Texture Fragmentation and Reconstruction (TFR) algorithm, based on a split-and-merge paradigm, which provides a sequence of nested segmentation maps, at various scales of observation. Early experiments on several high-resolution test images confirm the potential of TFR, but there is room for further improvements under various points of view. In this paper we describe the TFR algorithm and, starting from the analysis of some critical results propose two new version that address and solve some of its weak points.