  Recently perfectly secure steganographic systems have been described for a
wide class of sources of covertexts. The speed of transmission of secret
information for these stegosystems is proportional to the length of the
covertext. In this work we show that there are sources of covertexts for which
such stegosystems do not exist. The key observation is that if the set of
possible covertexts has a maximal Kolmogorov complexity, then a high-speed
perfect stegosystem has to have complexity of the same order.
