  Exploiting a spectral criterion for a system not to be AT we give some new
examples of zero entropy systems without the AT property. Our examples include
those with finite spectral multiplicity -- in particular we show that the
system arising from the Rudin-Shapiro substitution is not AT. We also show that
some nil-rotations on a quotient of the Heisenberg group as well as some
(generalized) Gaussian systems are not AT. All known examples of non
AT-automorphisms contain a Lebesgue component in the spectrum.
