Future anthropogenic climate change in the Southern Hemisphere is likely to be driven by two opposing effects, stratospheric ozone recovery and increasing greenhouse gases. We examine simulations from two coupled climate models in which the details of these two forcings are known. While both models suggest that recent positive summertime trends in the Southern Annular Mode (SAM) will reverse sign over the coming decades as the ozone hole recovers, climate sensitivity appears to play a large role in modifying the strength of their SAM response. Similar relationships are found between climate sensitivity and SAM trends when the analysis is extended to transient CO2 simulations from other coupled models. Tropical upper tropospheric warming is found to be more relevant than polar stratospheric cooling to the intermodel variation in the SAM trends in CO2-only simulations.