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The analysis of JPEG double-compressed images is a problem largely studied by the multimedia forensics community, as it might be exploited, e.g., for tampering localization or source device identification. In many practical scenarios, like photos uploaded on blogs, on-line albums, and photo sharing web sites, images might be JPEG compressed several times. However, the identification of the number of compression stages applied to an image remains an open issue. We proposes a forensic method based on the analysis of the distribution of the first significant digits of the discrete cosine transform coefficients, which follow Benford's law in images compressed just once. Then, the detector is optimized and extended in order to identify accurately the number of compression stages applied to an image. The experimental validation considers up to four consecutive compression stages and shows that the proposed approach extends and outperforms the previously-published algorithms for double JPEG compression detection.