  If $X$ is a singular del Pezzo surface of degree $d$ over a finite field
$\mathbb{F}_{q}$ with only rational double point singularities, does there
always exist a smooth $\mathbb{F}_{q}$-point on $X$? We show that this is true
for $d\geq 3$ and give counterexamples in the case of $d=2$.
