  We continue our study of the class $\mathscr{C}(D)$, where $D$ is a uniform
ultrafilter on a cardinal $\kappa$ and $\mathscr{C}(D)$ is the class of all
pairs $(\theta_1, \theta_2),$ where $(\theta_1, \theta_2)$ is the cofinality of
a cut in $J^\kappa /D$ and $J$ is some $(\theta_1+\theta_2)^+$-saturated dense
linear order. We give a combinatorial characterization of the class
$\mathscr{C}(D)$. We also show that if $(\theta_1, \theta_2) \in
\mathscr{C}(D)$ and $D$ is $\aleph_1$-complete or $\theta_1 + \theta_2 >
2^\kappa,$ then $\theta_1=\theta_2.$
