  In a recent paper the first author established the uniqueness of photon
spheres, suitably defined, in static vacuum asymptotically flat spacetimes by
adapting Israel's proof of static black hole uniqueness. In this note we
establish uniqueness of photon spheres by adapting the argument of Bunting and
Masood-ul-Alam, which then allows certain assumptions to be relaxed. In
particular, multiple photon spheres are allowed a priori.
  As a consequence of our result, we can rule out the existence of static
configurations involving multiple "very compact" bodies and black holes.
