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 self-consistently 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 caused by 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.