We study how the vertical distribution of relative humidity (RH) affects climate sensitivity, even if it remains unchanged with warming. Using a radiative-convective equilibrium model, we show that the climate sensitivity depends on the shape of a fixed vertical distribution of humidity, tending to be higher for atmospheres with higher humidity. We interpret these effects in terms of the effective emission height of water vapor. Differences in the vertical distribution of RH are shown to explain a large part of the 0 to 30% differences in clear-sky sensitivity seen in climate and storm-resolving models. The results imply that convective aggregation reduces climate sensitivity, even when the degree of aggregation does not change with warming. Combining our findings with relative humidity trends in reanalysis data shows a tendency toward Earth becoming more sensitive to forcing over time. These trends and their height variation merit further study.