Intense flares at cm-wavelengths reaching levels of tens of Jy have been observed from Cygnus X-3 for many years. This active high mass X-ray binary also has periods of quenching before major outbursts, and has minor flares at levels of a few hundred mJy. In this paper we show that the minor flares have much shorter rise times and durations suggesting more rapid expansion of the synchrotron radiation emitting material than in the strong flares. They also appear closer to the binary, whereas the large flares form a more developed jet. Calculations of physical conditions show that the minor out-bursts have lower minimum power but have larger magnetic fields and energy densities than the major flares. Minor flares can occur while a major flare is in progress, suggesting an indirect coupling between them. The spectral evolution of the minor flares can be explained by either an expanding synchrotron source or a shock model. The possibility that there is a brightening zone as in SS433 is explored.