We consider the Einstein constraints on asymptotically Euclidean manifolds
M of dimension n greater than or equal to 3 with sources of both scaled and
unsealed types. We extend to asymptotically Euclidean manifolds the constr
uctive method of proof of existence. We also treat discontinuous scaled sou
rces. In the last section we obtain new results in the case of non-constant
mean curvature.