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This paper aims at reducing the embedding distortion of prediction error expansion reversible watermarking. Instead of embedding the entire expanded difference into the current pixel, the difference is split between the current pixel and its prediction context. The modification of the context generates an increase of the following prediction errors. Global optimization is obtained by tuning the amount of data embedded into context pixels. Prediction error expansion reversible watermarking schemes based on median edge detector (MED), gradient-adjusted predictor (GAP), and a simplified GAP version, SGAP, are investigated. Improvements are obtained for all the predictors. Notably good results are obtained for SGAP-based schemes. The improved SGAP appears to outperform GAP-based reversible watermarking.