This study uses an analytical model, based on the cooling-to-space approximation, and a fixed dynamical heating model to investigate the structure of the stratospheric cooling that occurs in response to a uniform increase in stratospheric water vapour (SWV). At all latitudes, the largest cooling occurs in the lower stratosphere and decreases in magnitude with height. The cooling is strongly enhanced in the Extratropics compared to the Tropics. This is markedly different to the case of an increase in CO 2 , which causes maximum cooling near the stratopause and a small warming in the tropical lower stratosphere. The qualitative differences in the structure of the cooling can be explained by the smaller opacity of water vapour bands in the stratosphere compared to CO 2 . The small opacity means that the magnitude of the initial heating rate perturbation only decreases by a factor of four between the upper and lower stratosphere for a SWV perturbation. Therefore, to balance the heating rate perturbation, the largest temperature change is required in the lower stratosphere. Increasing the background concentration of SWV causes the water vapour bands to become more opaque. For a SWV perturbation applied to a background SWV concentration ≥30 ppmv, the heating rate perturbation and temperature change structurally resemble those from an increase in CO 2 . In the Extratropics, the lower height of the tropopause is found to cause the enhancement in the cooling at those latitudes. By controlling the depth of atmosphere which adjusts to the SWV perturbation, the tropopause height affects the net exchange of radiation between the layers in the stratosphere as they cool. The latitudinal gradient in upwelling infrared radiation at the tropopause and variations in the background temperature are found to have only a minor effect on the structure of the stratospheric temperature response to a change in SWV. Copyright c 2011 Royal Meteorological Society Key Words: radiative transfer; fixed dynamical heating; stratospheric water vapour