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We present a statistical attribution analysis of the changes in global annual average thermospheric mass density and ionospheric total electron content (TEC) between the cycle 22/23 solar minimum (which occurred at epoch 1996.4) and the prolonged cycle 23/24 minimum (2008.8). The mass density data are derived from orbital drag, and the TEC data are derived from ground-based GPS receivers. The interminima change in mass density was -36\% relative to the 1996.4 yearly average. Considering each multiplicative forcing independently, lower average geomagnetic activity during the cycle 23/24 minimum produced an interminima density change of at least -14\%, solar extreme ultraviolet (EUV) irradiance forcing produced a density change of -1\% to -13\%, and changes in thermospheric CO₂concentration produced a density change of -5\%. There was essentially no interminima change in global TEC derived from ground-based GPS receivers or space-based altimeters, even though past behavior suggests that it should have changed -3\% (0.2 TEC units (1 TECU = 10¹⁶ el m^-2)) in response to lower geomagnetic activity and -1\% to -9\% (0.1\textendash0.8 TECU) in response to lower EUV irradiance. There is large uncertainty in the interminima change of solar EUV irradiance; the mass density and TEC data suggest a plausible range of 0\% to -6\%.