Since the introduction of adaptive steganography, most of the recent research works seek at designing cost functions that are evaluated against steganalysis methods. While those approaches have been successful, they rely on intuitive principles and ad-hoc costs associated with each pixel or Discrete Cosine Transform (DCT) coefficient. Beyond the empirical assessments, the insights one can get from such approaches are very limited. On the opposite, this paper presents an original method for steganography in JPEG images that exploits a statistical model of the DCT coefficients. Within the framework of hypothesis testing theory, we use a statistical model of covers to derive the analytical expression of the most powerful detector. The objective of the steganographer is to minimize the statistical performance of this “omniscient detector” which represents a “worst-case” scenario for security. This paper shows how this method allows designing effective steganography, in terms of both security and computational complexity, in the two main use cases: when having only one single JPEG image and when the uncompressed image is available, case also known as Side-Informed (SI). A wide range of numerical comparisons shows that the proposed method outperforms the current state-of-the-art especially against the latest and most accurate steganalysis approaches based on Deep Learning.