  We continue our investigation =of Shelah's interpretability orders
$\trianglelefteq^*_\kappa$ as well as the new orders
$\trianglelefteq^\times_\kappa$. In particular, we give streamlined proofs of
the existence of minimal unstable, unsimple and nonlow theories in these
orders, and we give a similar analysis of the hypergraph examples $T_{n, k}$ of
Hrushovski. We also prove that if $\mathcal{B}$ is a complete Boolean algebra
with the $\lambda$-c.c., then no nonprincipal ultrafilter on $\mathcal{U}$
$\lambda^+$-saturates any unsimple theory.
