  We prove packing stability for any closed symplectic manifold with rational
cohomology class. This will rely on a general symplectic embedding result for
ellipsoids which assumes only that there is no volume obstruction and that the
domain is sufficiently thin relative to the target. We also obtain easily
computable bounds for the Embedded Contact Homology capacities which are
sufficient to imply the existence of some volume preserving embeddings in
dimension 4.
