The long-term transitions of the black hole candidate Cygnus X-1 (between the states gamma1, gamma2, an gamma3) include the occasional appearance of a strong approximately MeV bump (gamma1), whose strength appears to be anticorrelated with the continuum flux (less than or similar to 400 keV) due to the Compton upscattering of cold disk photons by the inner, hot corona. We develop a self-consistent disk picture that accounts naturally for these transitions and their corresponding spectral variations. We argue that the bump is due to the self-Comptonization of bremsstrahlung photons emitted predominantly near the plane of the corona itself. Our results suggest that a decrease by a factor of almost-equal-to 2 in the viscosity parameter alpha is responsible for quenching this bump and driving the system to the gamma2 state, whereas a transition from gamma2 to gamma3 appears to be induced by an increase of about 25% in the accretion rate M. In view of the fact that most of the transitions observed in this source seem to be of the gamma2-gamma3 variety, we conclude that much of the long-term gamma-ray spectral variability in Cygnus X-1 is due to these small fluctuations in M. The unusual appearance of the gamma1 state apparently reflects a change in the dissipative processes within the disk.