  In this paper we pursue the work initiated in \cite{Bahuaud,
BahuaudGicquaud}: study the extent to which conformally compact asymptotically
hyperbolic metrics can be characterized intrinsically. We show how the decay
rate of the sectional curvature to -1 controls the H\"older regularity of the
compactified metric. To this end, we construct harmonic coordinates that
satisfy some Neumann-type condition at infinity. Combined with a new
integration argument, this permits us to recover to a large extent our previous
result without any decay assumption on the covariant derivatives of the Riemann
tensor. We believe that our result is optimal.
