The current art in schemes using deflection criterion such as MiPOD for JPEG steganography is either under-performing or on par with distortion-based schemes. We link this lack of performance to a poor estimation of the variance of the model of the noise on the cover image. In this paper, we propose a method to better estimate the variances of DCT coefficients by taking into account the dependencies between pixels that come from the development pipeline. Using this estimate, we are able to extend statistically-informed steganographic schemesto the JPEG domain while significantly outperform-ing the current state-of-the-art JPEG steganography. An extension of Gaussian Embedding in the JPEG domain using quantization error as side-information is also formulated and shown to attain state-of-the-art performances.