The atmospheric circulation response to CO₂ doubling in various versions of an atmospheric general circulation model (AGCM) without a well-resolved stratosphere (“low-top” model), is compared to the response in a version of the same AGCM with a well-resolved stratosphere (“high-top” model). The doubled CO₂ response of the “best-tuned” (i.e. operational) low-top model version is significantly different from that in the best-tuned high-top model version. Additional experiments show that this difference is not caused by the model lid height, but instead can be mainly attributed to differences in the settings of parameterized orographic gravity-wave drag which control the strength of the zonal wind in the mid- to high-latitude lower stratosphere and the mean sea-level pressure distribution. These findings suggest a link between the strength of the winds in the mid- to high-latitude lower stratosphere and tropospheric annular mode responses, and have implications for how to proceed with high-top low-top model intercomparisons.