  A graph is $d$-orientable if its edges can be oriented so that the maximum
in-degree of the resulting digraph is at most $d$. $d$-orientability is a
well-studied concept with close connections to fundamental graph-theoretic
notions and applications as a load balancing problem. In this paper we consider
the d-ORIENTABLE DELETION problem: given a graph $G=(V,E)$, delete the minimum
number of vertices to make $G$ $d$-orientable. We contribute a number of
results that improve the state of the art on this problem. Specifically:
  - We show that the problem is W[2]-hard and $\log n$-inapproximable with
respect to $k$, the number of deleted vertices. This closes the gap in the
problem's approximability.
  - We completely characterize the parameterized complexity of the problem on
chordal graphs: it is FPT parameterized by $d+k$, but W-hard for each of the
parameters $d,k$ separately.
  - We show that, under the SETH, for all $d,\epsilon$, the problem does not
admit a $(d+2-\epsilon)^{tw}$, algorithm where $tw$ is the graph's treewidth,
resolving as a special case an open problem on the complexity of PSEUDOFOREST
DELETION.
  - We show that the problem is W-hard parameterized by the input graph's
clique-width. Complementing this, we provide an algorithm running in time
$d^{O(d\cdot cw)}$, showing that the problem is FPT by $d+cw$, and improving
the previously best known algorithm for this case.
