  We study the correlation structure of separable and classical states in 2x2-
and 2x3-dimensional quantum systems with fixed spectra. Even for such simple
systems the maximal correlation - as measured by mutual information - over the
set of unitarily accessible separable states is highly non-trivial to compute;
however for the 2x2 case a particular class of spectra admits full analysis and
allows us to contrast classical states with more general separable states. We
analyse a particular entropic partial order on the set of spectra and prove for
the qubit-qutrit case that this partial order alone picks out a unique
classical maximum state for mutual information. Moreover the 2x3 case is the
largest system with such a property.
