  We generalize and simplify an earlier approach. In three dimensions we
present the most general averaging formula in lowest order which respects the
requirements of covariance. It involves a bitensor, made up of a basis of six
tensors, and contains three arbitrary functions, which are only restricted by
their behavior near the origin. The averaging formula can also be applied to
the Einstein tensor. If one of the functions is put equal to zero one has the
pleasant property that the Einstein tensor of the averaged metric is identical
to the averaged Einstein tensor. We also present a simple covariant extension
to static perturbations in four dimensions. Unfortunately the result for the
Einstein tensor cannot be extended to the four dimensional case.
