This proposed scheme reversibly embeds data into image prediction-errors by using histogram-pair method with double thresholds (embedding threshold and fluctuation threshold). 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. Only when both thresholds are satisfied the reversible data hiding is carried out. Image gray level histogram modification is conducted to shrink the image histogram towards the center to avoid underflow and/or overflow only when this is necessary. The required bookkeeping data are embedded together with pure payload for original image recovery late. The experimental results have demonstrated that the proposed scheme outperforms recently published reversible image data hiding schemes in terms of the highest PSNR of marked image vs. original image at given pure payloads.