  We investigate what collections of c.e.\ Turing degrees can be realised as
the collection of elements of a separating $\Pi^0_1$ class of c.e.\ degree. We
show that for every c.e.\ degree $\mathbf{c}$, the collection $\{\mathbf{c},
\mathbf{0}'\}$ can be thus realized. We also rule out several attempts at
constructing separating classes realizing a unique c.e.\ degree. For example,
we show that there is no \emph{super-maximal} pair: disjoint c.e.\ sets $A$ and
$B$ whose separating class is infinite, but every separator of c.e.\ degree is
a finite variant of either $A$ or $\overline{B}$.
