  Let (M,g) a compact Riemannian $n$-dimensional manifold with umbilic
boundary. It is well know that, under certain hypothesis, in the conformal
class of g there are scalar-flat metrics that have the boundary of M as a
constant mean curvature hypersurface. In this paper we prove that these metrics
are a compact set in the case of low dimensional manifolds, that is n=6,7,8,
provided that the Weyl tensor is always not vanishing on the boundary.
