  For the first time, detailed radiative transfer calculations of Comptonized
X-ray and gamma-ray radiation in a hot pair plasma above a cold accretion disk
are performed using two independent codes and methods. The simulations include
both energy and pair balance as well as reprocessing of the X- and gamma-rays
by the cold disk. We study both plane-parallel coronae as well as active
dissipation regions having shapes of hemispheres and pill boxes located on the
disk surface. It is shown, contrary to earlier claims, that plane-parallel
coronae in pair balance have difficulties in selfconsistently reproducing the
ranges of 2-20 keV spectral slopes, high energy cutoffs, and compactnesses
inferred from observations of type 1 Seyfert galaxies. Instead, the
observations are consistent with the X-rays coming from a number of individual
active regions located on the surface of the disk.
  A number of effects such as anisotropic Compton scattering, the reflection
hump, feedback to the soft photon source by reprocessing, and an active region
in pair equilibrium all conspire to produce the observed ranges of X-ray
slopes, high energy cutoffs, and compactnesses. The spread in spectral X-ray
slopes can be due to a spread in the properties of the active regions such as
their compactnesses and their elevations above the disk surface. Simplified
models invoking isotropic Comptonization in spherical clouds are no longer
sufficient when interpreting the data.
