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Reversible data hiding (RDH) with contrast enhancement (RDH-CE) is a special type of RDH in improving the subjective visual perception by enhancing the image contrast during the process of data embedding. In RDH-CE, data hiding is achieved via pairwise histogram expansion, and the embedding rate can be increased by performing multiple cycles of histogram expansions. However, when embedding rate gets high, human visible image degradation is observed. Previous work designed an upper bound of the embedding level for RDH-CE, which effectively avoids image over-sharping but offers limited embedding capacity. In this paper, a better tunable bound is designed to enhance the embedding capacity of RDH-CE by exploiting the characteristics of histogram distribution. Furthermore, the objective distortion introduced by histogram pre-shifting is minimized when the embedding level is no more than the upper bound, and the human visible degradation is minimized when the embedding level exceeds the limitation of the proposed upper bound. Experimental results validate that the proposed method provides appropriate upper bound of the embedding level, increases the effective embedding capacity and offers better image contrast. [ABSTRACT FROM AUTHOR]