We report flux densities for Cygnus X-3 at 2.25 and 8.3 GHz for 1988-1992 (2.7 and 8.1 GHz prior to 1989.75). These flux densities are presented on a scale which emphasizes the relationship between very low flux densities (<30 mJy) and the evolution of major flares in Cygnus X-3. The quiescent radio flux density of Cygnus X-3 was observed to drop from roughly 80 to 14 mJy +/- 6 mJy at 2.25 GHz and from 90 to 22 mJy +/- 9 mJy at 8.3 GHz during six pre-flare intervals from 1990 through 1992. The duration of unusually low flux density varied from three days to two months. Lower quiescent flux densities than normal (35-60 mJy) also occurred during periods of active small flaring (<1 Jy) but were not as well defined. These periods of very low flux density persist longer than the opacity which occurs for a few days after onset of the flare in the expanding synchrotron cloud model of Marscher & Brown [ApJ, 200, 719 (1975)] but may be explained by quenching of the quiescent radio emission during periods of heavy accretion prior to major radio flares [Kitamoto et al., A&A, 281, L85 (1994)].