The goal of steganography is to pass secret messages by disguising them as innocent-looking covertexts. Real world stegosystems are often broken because they make invalid assumptions about the system’s ability to sample covertexts. We examine whether it is possible to weaken this assumption. By modeling the covertext distribution as a stateful Markov process, we create a sliding scale between real world and provably secure stegosystems. We also show that insufficient knowledge of past states can have catastrophic results.