  We compute the indicial roots of the Lichnerowicz Laplacian on Ricci-flat
cones and give a detailed description of the corresponding radially homogeneous
tensor fields in its kernel. For a Ricci-flat conifold $(M,g)$ which may have
asymptotically conical as well as conically singular ends, we compute at each
end a lower bound for the order with which the metric converges to the tangent
cone. As a special subcase of our result, we show that any Ricci-flat ALE
manifold $(M^n,g)$ is of order $n$ and thereby close a small gap in a paper by
Cheeger and Tian.
