The current art of steganography shows that schemes using a deflection criterion (such as MiPOD) for JPEG steganography are usually subpar with respect to distortionbased schemes. We link this lack of performance to a poor estimation of the variance of the model of the noise on the cover image. However, this statistically-based method provides a better assessment of the detectability of hidden data as well as theoretical guarantees under a given model. In this paper, we propose a method to obtain better estimates of the variances of DCT coefficients by taking into account the dependencies introduced by development pipeline on pixels. A second method, which is a side-informed extension of Gaussian Embedding in the JPEG domain using quantization error as side-information, is also formulated and shown to achieve state-of-the-art performances. Eventually, the trade-off between noise and content complexity in steganography is thoroughly analyzed through the lenses of these two new methods using a wide range of numerical experiments.