We use global-average thermospheric total mass density, derived from the drag effect on the orbits of many space objects, to study the behavior of the thermosphere during the prolonged minimum in solar activity between cycles 23 and 24. During 2007–2009 thermospheric densities at a fiducial altitude of 400 km were the lowest observed in the 43-year database, and were anomalously low, by 10–30%, compared with climatologically expected levels. The density anomalies appear to have commenced before 2006, well before the cycle 23/24 minimum, and are larger than expected from enhanced thermospheric cooling by increasing concentrations of CO₂. The height dependence of the mass density anomalies suggests that they are attributable to a combination of lower-than-expected exospheric temperature (−14 K) and reductions in the number density of atomic oxygen (−12%) and other species (−3%) near the base of the diffusive portion of the thermosphere.