  In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed
that ultra-compact objects, self-gravitating horizonless solutions of the
Einstein field equations which have a light ring, must possess at least {\it
two} (and, in general, an even number of) light rings, of which the inner one
is {\it stable}. In the present compact paper we explicitly prove that, while
this intriguing theorem is generally true, there is an important exception in
the presence of degenerate light rings which, in the spherically symmetric
static case, are characterized by the simple dimensionless relation $8\pi
r^2_{\gamma}(\rho+p_{\text{T}})=1$ [here $r_{\gamma}$ is the radius of the
light ring and $\{\rho,p_{\text{T}}\}$ are respectively the energy density and
tangential pressure of the matter fields]. Ultra-compact objects which belong
to this unique family can have an {\it odd} number of light rings. As a
concrete example, we show that spherically symmetric constant density stars
with dimensionless compactness $M/R=1/3$ possess only {\it one} light ring
which, interestingly, is shown to be {\it unstable}.
