In this work we aim to design a steganographic scheme undetectable by the Reverse JPEG Compatibility Attack (RJCA). The RJCA, while only effective for JPEG images compressed with quality factors 99 and 100, was shown to work mainly due to change in variance of the rounding errors after decompression of the DCT coefficients, which is induced by embedding changes incompatible with the JPEG format. One remedy to preserve the aforementioned format is utilizing during the embedding the rounding errors created during the JPEG compression, but no steganographic method is known to be resilient to RJCA without this knowledge. Inspecting the effect of embedding changes on both variance and mean of decompression rounding errors, we propose a steganographic method allowing resistance against RJCA without any side-information. To reach this goal, we propose a distortion metric making all embedding changes within a DCT block dependent, resulting in a lattice-based embedding. Then it turns out it is enough to cleverly pick the side of the (binary) embedding changes through inspection of their effect on the variance of decompression rounding errors and simply use constant costs in order to enforce their sparsity across DCT blocks. To increase security against detectors in the spatial (pixel) domain, we show an easy way of combining the proposed methodology with steganography designed for spatial domain security, further improving the undetectability for quality factor 99. The improvements over existing non-informed steganography are up to 40% in terms of detector's accuracy.