Future changes in orographic precipitation will have important consequences for societies and ecosystems near mountain ranges. Here we use a simple numerical model to evaluate the response of orographic precipitation to surface warming under idealized conditions representative of the strongest orographic storms. We find an upward shift in the pattern of condensation with warming, caused by larger fractional changes in condensation at low temperature and amplified warming aloft. As a result, the distribution of precipitation shifts downwind, causing larger fractional changes in precipitation on the lee slope than on the windward slope. Total precipitation is found to increase by a smaller fraction than near‐surface water vapor, in contrast to expected changes in other types of extreme precipitation. Factors limiting the increase in orographic precipitation include the pattern of windward ascent, leeside evaporation, and thermodynamic constraints on the change in condensation with temperature. Key Points Condensation shifts upward with warming due to basic thermodynamics Leeside precipitation is more sensitive to warming than windward precipitation The increase in extreme precipitation may be lower in mountains than elsewhere