This proposed scheme reversibly embeds data into image prediction-errors by using histogram-pair method with the following four thresholds for optimal performance: embedding threshold, fluctuation threshold, left- and right-histogram shrinking thresholds. The embedding threshold is used to select only those prediction-errors, whose magnitude does not exceed this threshold, for possible reversible data hiding. The fluctuation threshold is used to select only those prediction-errors, whose associated neighbor fluctuation does not exceed this threshold, for possible reversible data hiding. The left- and right-histogram shrinking thresholds are used to possibly shrink histogram from the left and right, respectively, by a certain amount for reversible data hiding. Only when all of four thresholds are satisfied the reversible data hiding is carried out. Different from our previous work, the image gray level histogram shrinking towards the center is not only for avoiding underflow and/or overflow but also for optimum performance. The required bookkeeping data are embedded together with pure payload for original image recovery. The experimental results on four popularly utilized test images (Lena, Barbara, Baboon, Airplane) and one of the JPEG2000 test image (Woman, whose histogram does not have zero points in the whole range of gray levels, and has peaks at its both ends) have demonstrated that the proposed scheme outperforms recently published reversible image data hiding schemes in terms of the highest PSNR of marked image verses original image at given pure payloads.