In some regions, reducing aerosol ammonium nitrate (NH4NO3) concentrations may substantially improve air quality. This can be accomplished by reductions in precursor emissions, such as nitrogen oxides (NO) to lower nitric acid (HNO3) that partitions to the aerosol, or reductions in ammonia (NH3) to lower particle pH and keep HNO3 in the gas phase. Using the ISORROPIA-II thermodynamic aerosol model and detailed observational data sets, we explore the sensitivity of aerosol NH4NO3 to gas-phase NH3 and NOx controls for a number of contrasting locations, including Europe, the United States, and China. NOx control is always effective, whereas the aerosol response to NH3 control is highly nonlinear and only becomes effective at a thermodynamic sweet spot. The analysis provides a conceptual framework and fundamental evaluation on the relative value of NOx versus NH3 control and demonstrates the relevance of pH as an air quality parameter. We find that, regardless of the locations examined, it is only when ambient particle pH drops below an approximate critical value of 3 (slightly higher in warm and slightly lower in cold seasons) that NH3 reduction leads to an effective response in PM2.5 mass. The required amount of NH3 reduction to reach the critical pH and efficiently decrease NH4NO3 at different sites is assessed. Owing to the linkage between NH3 emissions and agricultural productivity, the substantial NH3 reduction required in some locations may not be feasible. Finally, controlling NH3 emissions to increase aerosol acidity and evaporate NH4NO3 will have other effects, beyond reduction of PM2.5 NH4NO3, such as increasing aerosol toxicity and potentially altering the deposition patterns of nitrogen and trace nutrients. © 2018 Author(s).