  The most difficult counterterms to construct in any supersymmetric theory are
those that cannot be written as full superspace integrals of gauge-invariant
integrands. In $D=4$ maximal supergravity it has been known for some time that
there are just three of these at the linearised level. In this article we
discuss these counterterms again from the point of view of representations of
the superconformal group. In particular, we show that the only independent
invariants constructed from shortened superconformal multiplets in $D=4$ are
BPS.
