Nitrous oxide (N2O) is one of the top three greenhouse gases whose emissions may be brought under control through the Framework Convention on Climate Change. Current understanding of its global budget, including the balance of natural and anthropogenic sources, is largely based on the atmospheric losses calculated with chemical models. A representative one-dimensional model used here describes the photochemical coupling between N2O and stratospheric ozone (O-3), which can easily be decomposed into its natural modes. The primary, longest lived mode describes most of the atmospheric perturbation due to anthropogenic N2O sources, and this pattern may be observable. The photolytic link between O-3 and N2O is identified as the mechanism causing this mode to decay 10 to 15 percent more rapidly than the N2O mean atmospheric lifetime, affecting the inference of anthropogenic sources.