  We investigate the $a$-numbers of $\mathbb{Z}/p^2\mathbb{Z}$-covers in
characteristic $p>2$ and extend a technique originally introduced by Farnell
and Pries for $\mathbb{Z}/p\mathbb{Z}$-covers. As an application of our
approach, we demonstrate that the $a$-numbers of ``minimal''
$\mathbb{Z}/9\mathbb{Z}$-covers can be deduced from the associated branching
datum.
