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Although ScaScraIH  is able to scalably scramble image/video and offer scalable carrier capacity for reversible data embedding , the product of ScaScraIH suffers from bitstream size increment of ~ 9.17% on average. The main cause of bitstream size increment in ScaScraIH is storing the number of nonzero coefficients in each 8 × 8 block which is utilized during the descrambling process. This paper proposes two techniques in suppressing bitstream size increment for ScaScraIH. The first technique exploits the distribution of nonzero DCT coefficients in the image to construct a scanning order, aiming to shorten the distance between nonzero coefficients in a block. For the second technique, combination of predictive and entropy coding is used to encode the number of nonzero coefficients. Experiments are conducted by using standard test images to verify the effectiveness of both techniques in suppressing bitstream size increment. On average, bitstream size increment is significantly suppressed to ~ 0.91%, with some of the processed images assuming smaller bitstream size than its original counter part.