Ice-core measurements indicate that atmospheric CO2 concentrations during glacial periods were consistently about 80 parts per million lower than during interglacial periods. Previous explanations for this observation have typically had difficulty accounting for either the estimated glacial O2 concentrations in the deep sea, 13C/12C ratios in Antarctic surface waters, or the depth of calcite saturation; also lacking is an explanation for the strong link between atmospheric CO2 and Antarctic air temperature. There is growing evidence that the amount of deep water upwelling at low latitudes is significantly overestimated in most ocean general circulation models and simpler box models previously used to investigate this problem. Here we use a box model with deep-water upwelling confined to south of 55 degrees S to investigate the glacial-interglacial linkages between Antarctic air temperature and atmospheric CO2 variations. We suggest that low glacial atmospheric CO2 levels might result from reduced deep-water ventilation associated with either year-round Antarctic sea-ice coverage, or wintertime coverage combined with ice-induced stratification during the summer. The model presented here reproduces 67 parts per million of the observed glacial-interglacial CO2 difference, as a result of reduced air-sea gas exchange in the Antarctic region, and is generally consistent with the additional observational constraints.