Can entropicly secure encryption algorithms be used on low-entropy messages by adding noise
Here is the problem: if $M$ has low entropy (for example, if the attacker has side information that narrows $M$ down to just two possible messages), then conditioned on $M+K$, the key $K$ also has low entropy (there are only two possibilities for $K$). If the eavesdropper stores the first message (which was an encryption of $K$), then she can use it to figure out which of the two candidate values for $K$ is plausible (i.e. is consistent with some short key $K_{RW}$) once she sees the second message.

This problem is essentially unavoidable: taken together, the two messages form an encryption of $M$ (the fact that they were sent separately doesn't affect a passive eavesdropper who sees both). It is easy to show that, using only a short key, one cannot achieve even Russell and Wang's relaxed notion of security in a setting where $M$ has low entropy. 

For a lower bound on the key length (as well as further constructions), see Dodis and Smith: https://eprint.iacr.org/2004/219
[Disclaimer: I am an author.]