Steganography studies methods to not only protect the confidentiality of messages but also to conceal the very act of message transmission. Prior provably secure stegosystems are predominantly constructed based on a rejection sampling technique which achieves an encoding rate inversely proportional to the min-entropy of the cover channel. Furthermore, while replayable chosen-covertext attack (RCCA) secure stegosystems for general channels can be constructed based on standard cryptographic assumptions, it is known [Berndt and Liśkiewicz, EUROCRYPT’18] that achieving (standard) CCA-security for channels with memory in the so-called non-look-ahead model is in general impossible and the only known CCA-secure construction crucially relies on the channels being memoryless. In this work, we show that the impossibility on CCA-secure stegosystems can be circumvented, in the random oracle model, by dropping the non-look-ahead restriction and by restricting to a natural class of channels which we call “partially sampleable channels”. These capture channels which partly consist of explicitly sampleable distributions, such as Gaussian sensor noise of digital photographs. To achieve a high encoding rate, we extend the formalisation of stegosystems to capture a technique known as “cover-source switching” in the practical steganography literature. This allows us to construct CCA-secure stegosystems for Gaussian channels using Gaussian preimage sampling techniques borrowed from lattice-based cryptography, which can theoretically achieve an embedding rate of \(1/\omega (\log \log \lambda )\) regardless of the min-entropy of the channel. Our prototype implementation suggests that our scheme is practical, achieving an embedding rate of 24.7% in 24-megapixel RAW images in around 1 min per image.