The structural response of vitreous silica to changes in temperature and pressure is of fundamental importance in earth and materials sciences and is largely controlled by the ring-size distribution that controls the topology of the structure. The 3- and 4-membered rings constitute only a small fraction of the structure but are known to be sensitive to and increase in concentration with increasing pressure and temperature. We present new experimental results that show a sudden reversal in the temperature dependence of the concentrations of these rings near the recently discovered density minimum of vitreous silica. These results invalidate our conventional wisdom regarding the entropically stabilized, defect-like behavior of the small rings and indicate that these rings are possibly key players in controlling the density of silica.