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This paper proposes two data hiding approaches using compressed MPEG video. The first approach hides message bits by modulating the quantization scale of a constant bitrate video. A payload of one message bit per macroblock is achieved. A second order multivariate regression is used to find an association between macroblock-level feature variables and the values of a hidden message bit. The regression model is then used by the decoder to predict the values of the hidden message bits with very high prediction accuracy. The second approach uses the flexible macroblock ordering feature of H.264/AVC to hide message bits. Macroblocks are assigned to arbitrary slice groups according to the content of the message bits to be hidden. A maximum payload of three message bits per macroblock is achieved. The proposed solutions are analyzed in terms of message extraction accuracy, message payload, excessive bitrate and quality distortion. Comparisons with previous work reveal that the proposed solutions are superior in terms of message payload while causing less distortion and compression overhead.