The reverse JPEG compatibility attack has recently been introduced as a very accurate and universal steganalysis algorithm for JPEG images with quality 99 or 100. The limitation to these two largest qualities appears fundamental as the prior work on this topic suggests. In this paper, we provide mathematical analysis and demonstrate experimentally that this attack can be extended to double compressed images when the first compression quality is 93 or larger and the second quality equal or larger than the first quality. Comparisons with stateof-the-art deep convolutional neural networks as well as detectors built in the JPEG domain show the merit of this work.