  A distinguished family of completely prime primitive ideals in the universal
enveloping algebra of a reductive Lie algebra ${\mathfrak g}$ over ${\mathbb
C}$ are those ideals constructed from one-dimensional representations of finite
$W$-algebras. We refer to these ideals as Losev--Premet ideals. For ${\mathfrak
g}$ simple of classical type, we prove that for a Losev-Premet ideal $I$ in
$U({\mathfrak g})$, there exists a Losev-Premet ideal $I_0$ for a certain Levi
subalgebra ${\mathfrak g}_0$ of ${\mathfrak g}$ such that associated variety of
$I_0$ is the closure of a rigid nilpotent orbit in ${\mathfrak g}_0$ and $I$ is
obtained from $I_0$ by parabolic induction. This is deduced from the
corresponding statement about one-dimensional representations of finite
$W$-algebras.
