  Let $G$ be a $d$-regular graph and let $F\subseteq\{0, 1, 2, \ldots, d\}$ be
a list of forbidden out-degrees. Akbari, Dalirrooyfard, Ehsani, Ozeki, and
Sherkati conjectured that if $|F|<\tfrac{1}{2}d$, then $G$ should admit an
$F$-avoiding orientation, i.e., an orientation where no out-degrees are in the
forbidden list $F$. The conjecture is known for $d\leq 4$ due to work of Ma and
Lu, and here we extend this to $d\leq 6$. The conjecture has also been studied
in a generalized version, where $d, F$ are changed from constant values to
functions $d(v), F(v)$ that vary over all $v\in V(G)$. We provide support for
this generalized version by verifying it for some new cases, including when $G$
is 2-degenerate and when every $F(v)$ has some specific structure.
