  We say that a pure $d$-dimensional simplicial complex $\Delta$ on $n$
vertices is \emph{shelling completable} if $\Delta$ can be realized as the
initial sequence of some shelling of $\Delta_{n-1}^{(d)}$, the $d$-skeleton of
the $(n-1)$-dimensional simplex. A well-known conjecture of Simon posits that
any shellable complex is shelling completable. In this note we prove that
vertex decomposable complexes are shelling completable. In fact we show that if
$\Delta$ is a vertex decomposable complex then there exists an ordering of its
ground set $V$ such that adding the revlex smallest missing $(d+1)$-subset of
$V$ results in a complex that is again vertex decomposable. We explore
applications to matroids and shifted complexes, as well as connections to
ridge-chordal complexes and $k$-decomposability. We also show that if $\Delta$
is a $d$-dimensional complex on at most $d+3$ vertices then the notions of
shellable, vertex decomposable, shelling completable, and extendably shellable
are all equivalent.
