Most current steganographic schemes embed the secret payload by minimizing a heuristically defined distortion. Similarly, their security is evaluated empirically using classifiers equipped with rich image models. In this paper, we pursue an alternative approach based on a locally-estimated multivariate Gaussian cover image model that is sufficiently simple to derive a closed-form expression for the power of the most powerful detector of content-adaptive LSB matching but, at the same time, complex enough to capture the non-stationary character of natural images. We show that when the cover model estimator is properly chosen, state-of-the-art performance can be obtained. The closed-form expression for detectability within the chosen model is used to obtain new fundamental insight regarding the performance limits of empirical steganalysis detectors built as classifiers. In particular, we consider a novel detectability-limited sender and estimate the secure payload of individual images.