  We study states of large charge density in integrable conformal coset models.
For the O(2) coset, we consider two different S-matrices, one corresponding to
a Thirring mass perturbation and the other to the continuation to O(2+epsilon).
The former leads to simplification in the conformal limit; the latter gives a
more complicated description of the O(2) system, with a large zero mode sector
in addition to the right- and left-movers. We argue that for the conformal
O(2+2M|2M) supergroup coset, the S-matrix is given by the analog of the
O(2+epsilon) construction.
