We used the Goddard Space Flight Center (GSFC) global two-dimensional (2D) atmospheric model to investigate the stratospheric ozone response to a proposed geoengineering activity wherein a reduced top-of-atmosphere (TOA) solar irradiance is imposed to help counteract a quadrupled CO2 atmosphere. This study is similar to the Geoengineering Model Intercomparison Project (GeoMIP) Experiment G1. Three primary simulations were completed with the GSFC 2D model to examine this possibility: (A) a pre-industrial atmosphere with a boundary condition of 285 ppmv CO2 (piControl); (B) a base future atmosphere with 1140 ppmv CO2 (abrupt4xCO2); and (C) a perturbed future atmosphere with 1140 ppmv CO2 and a 4% reduction in the TOA total solar irradiance (G1). We found huge ozone enhancements throughout most of the stratosphere (up to 40%) as a result of a large computed temperature decrease (up to 18 K) when CO2 was quadrupled (compare simulation abrupt4xCO2 to piControl). Further, we found that ozone will additionally increase (up to 5%) throughout most of the stratosphere with total ozone increases of 1–2.5% as a result of a reduction in TOA total solar irradiance (compare simulation G1 to abrupt4xCO2). Decreases of atomic oxygen and temperature are the main drivers of this computed ozone enhancement from a reduction in TOA total solar irradiance.