[en] Recent Ginga observations of the Seyfert 1 galaxies NGC 4051 and MCG 6-30-15 show a positive correlation between the 2-10 keV luminosity and photon spectral index α. Similar behavior has also been reported in Exosat and Einstein observations of other active galactic nuclei, and is suggested in hard x-ray low-state data of the galactic black-hole candidate Cygnus X-1. A two-temperature thermal Comptonization model with internal soft-photon production provides a simple explanation for this correlation. The electron temperature, determined by a balance between ion heating and radiative cooling, decreases in response to an enhancement of the soft photon flux, resulting in a softening of the spectrum and an increase in the soft x-ray luminosity. The bulk of the soft photons are produced through pion production in collisions between the hot ions. Pivoting of the spectrum at photon energies var-epsilon > 50 keV is a consequence of variations in the ion temperature. An important test of the model would be time correlations between soft and hard x-ray bands. 17 refs., 9 figs., 1 tab