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This paper focuses on images whose content has been modified by means of a cut & paste operation. By relying on an existing scheme for the detection of double JPEG compressed images with desynchronized grids, we propose two algorithms for the detection of image regions that have been transplanted from another image. The proposed methods work whenever the pasted region is extracted from a JPEG compressed image and inserted in a target image that is subsequently compressed with a quality factor larger than that used to compress the source image. The new methods are intended as a complement to previous works relying on the detection of artifacts introduced by double JPEG compression with aligned compression grids. The experiments we carried out show the good performance of the novel schemes, the second one providing better results at a lower complexity thanks to the incorporation within the detection process of some information regarding the actual image content.