  We study the spectrum, the massless S-matrices and the ground-state energy of
the flows between successive minimal models of conformal field theory, and
within the sine-Gordon model with imaginary coefficient of the cosine term
(related to the minimal models by ``truncation''). For the minimal models, we
find exact S-matrices which describe the scattering of massless kinks, and show
using the thermodynamic Bethe ansatz that the resulting non-perturbative
c-function (defined by the Casimir energy on a cylinder) flows appropriately
between the two theories, as conjectured earlier. For the non-unitary
sine-Gordon model, we find unusual behavior. For the range of couplings we can
study analytically, the natural S-matrix deduced from the minimal one by
``undoing'' the quantum-group truncation does not reproduce the proper
c-function with the TBA. It does, however, describe the correct properties of
the model in a magnetic field.
