  Every simple Hermitian Lie group has a unique family of spherical
representations induced from a maximal parabolic subgroup whose unipotent
radical is a Heisenberg group. For most Hermitian groups, this family contains
a complementary series, and at its endpoint sits a proper unitarizable
subrepresentation. We show that this subrepresentation is next-to-minimal in
the sense that its associated variety is a next-to-minimal nilpotent coadjoint
orbit. Moreover, for the Hermitian groups $\operatorname{SO}_0(2,n)$ and
$E_{6(-14)}$ we study some branching problems of these next-to-minimal
representations.
