  We investigate the issues of unitarity and reality of the spectrum for the
imaginary coupled affine Toda field theories based on a_1(1) and a_2(2) and the
perturbed minimal models that arise from their various RSOS restrictions. We
show that while all theories based on a_1(1) have real spectra in finite
volume, the spectra of a_2(2) models is in general complex, with some
exceptions. We also correct the S matrices conjectured earlier for the phi(1,5)
perturbations of minimal models and give evidence for a conjecture that the
RSOS spectra can be obtained as suitable projections of the folded ATFTs in
finite volume.
