  We prove a refinement of Vogel's statement that the Vassiliev invariants of
knots coming from semisimple Lie algebras do not generate all Vassiliev
invariants. This refinement takes into account the second grading on Vassiliev
invariants induced by cabling of knots. As an application we get an
amelioration of the actually known lower bounds for the dimensions of the space
of Vassiliev invariants.
