  In this paper, we establish compactness results of some class of conformally
compact Einstein 4-manifolds. In the first part of the paper, we improve the
earlier results obtained by Chang-Ge. In the second part of the paper, as
applications, we derive some compactness results under perturbation conditions
when the L^2-norm of the Weyl curvature is small. We also derive the global
uniqueness of conformally compact Einstein metrics on the 4-Ball constructed in
the earlier work of Graham-Lee.
