  We present an elementary physical space argument to establish local
integrated decay estimates for the perturbed wave equation $\Box_g \phi =
\epsilon \beta^a \partial_a \phi$ on the exterior of the Schwarzschild geometry
$(\mathcal{M},g)$. Here $\beta$ is a regular vectorfield on $\mathcal{M}$
decaying suitably in space but not necessarily in time. The proof is formulated
to cover also perturbations of the Regge--Wheeler equation.
