  The observation of energetic X-ray emission from black holes, inconsistent
with thermal emission from an accretion disk, has long indicated the presence
of a "corona" around these objects. However, our knowledge of the geometry,
composition, and processes within black hole coronae is severely lacking. Basic
questions regarding their size and location are still a topic of debate. In
this letter, we show that for black holes with luminosities
$L\gtrsim10^{-2}L_{Edd}$ -- characteristic of many Seyferts, quasars, and
stellar-mass black holes (in their brighter states) -- advanced imaging and
timing data strongly favor X-ray emitting regions that are highly compact, and
only a few Gravitational radii above the accretion disk. The inclusion of a
large number of possible systematics uncertainties does not significantly
change this conclusion with our results still suggesting emission from within
$\sim20$\rg\ in all cases. This result favors coronal models wherein most of
the hard X-ray emission derives from magnetic reconnection in the innermost
disk and/or from processes in the compact base of a central, relativistic jet.
