Nitrous oxide (N2O) and methane (CH4) are chemically reactive greenhouse gases with well-documented atmospheric concentration increases that are attributable to anthropogenic activities. We quantified the link between N2O and CH4 emissions through the coupled chemistries of the stratosphere and troposphere. Specifically, we simulated the coupled perturbations of increased N2O abundance, leading to stratospheric ozone (O3) depletion, altered solar ultraviolet radiation, altered stratosphereto-troposphere O3 flux, increased tropospheric hydroxyl radical concentration, and finally lower concentrations of CH4. The ratio of CH4 per N2O change, –36% by mole fraction, offsets a fraction of the greenhouse effect attributable to N2O emissions. These CH4 decreases are tied to the 108-year chemical mode of N2O, which is nine times longer than the residence time of direct CH4 emissions.