  We study conditions on a $C^*$-dynamical system $(A,G,\alpha)$ under which
induction of primitive ideals (resp. irreducible representations) from
stabilizers for the action of $G$ on the primitive ideal space $\Prim(A)$ give
primitive ideals (resp. irreducible representations) of the crossed product
$A\rtimes_\alpha G$. The results build on earlier results of Sauvageot and
others, and will correct a (possibly overly optimistic) statement of the first
author.
