  We show that any asymptotically locally Euclidean (ALE) metric which is
obstruction-flat or extended obstruction-flat must be ALE of a certain optimal
order. Moreover, our proof applies to very general elliptic systems and in any
dimension $n \geq 3$. The proof is based on the technique of Cheeger-Tian for
Ricci-flat metrics. We also apply this method to obtain a singularity removal
theorem for (extended) obstruction-flat metrics with isolated $C^0$-orbifold
singular points.
