On reversing arcs to improve arc-connectivity

We show that if the arc-connectivity of a directed graph $D$ is at most $\lfloor \frac{k+1}{2}\rfloor$ and the reorientation of an arc set $F$ in $D$ results in a $k$-arc-connected directed graph then we can reorient one arc of $F$ without decreasing the arc-connectivity of $D\mathrm{.}$ This improves a result of Fukuda, Prodon, Sakuma and one of Ito et al. for $k\in \{2,3\}$.