Reduction of surface temperatures of the planet by injecting sulfate aerosols in the stratosphere has been suggested as an option to reduce the amount of human-induced climate warming. Several previous studies have shown that for a specified amount of injection, aerosols injected at a higher altitude in the stratosphere would produce more cooling because aerosol sedimentation would take longer. In this study, we isolate and assess the sensitivity of stratospheric aerosol radiative forcing and the resulting climate change to the altitude of the aerosol layer. We study this by prescribing a specified amount of sulfate aerosols, of a size typical of what is produced by volcanoes, distributed uniformly at different levels in the stratosphere. We find that stratospheric sulfate aerosols are more effective in cooling climate when they reside higher in the stratosphere. We explain this sensitivity in terms of effective radiative forcing: volcanic aerosols heat the stratospheric layers where they reside, altering stratospheric water vapor content, tropospheric stability, and clouds, and consequently the effective radiative forcing. We show that the magnitude of the effective radiative forcing is larger when aerosols are prescribed at higher altitudes and the differences in radiative forcing due to fast adjustment processes can account for a substantial part of the dependence of the amount of cooling on aerosol altitude. These altitude effects would be additional to dependences on aerosol microphysics, transport, and sedimentation, which are outside the scope of this study. The cooling effectiveness of stratospheric sulfate aerosols likely increases with the altitude of the aerosol layer both because aerosols higher in the stratosphere have larger effective radiative forcing and because they have higher stratospheric residence time; these two effects are likely to be of comparable importance.