We compare tracer observations made during the northern winter of 1999/2000 with the results of simulations with a three-dimensional chemical transport model, driven by assimilated winds. During the course of the winter, very low concentrations of tracers of tropospheric origin (such as N2O) descend into the lower stratosphere within the polar vortex. The altitude of origin of this air has been a matter of debate in the literature; by midwinter, both observations and model results indicate a significant fraction of mesospheric air in the lower stratosphere. Observations from aircraft and balloon flights reveal markers of mesospheric air within the Arctic vortex in the lower and middle stratosphere. An artificial tracer introduced into the model mesosphere at the start of winter descends (being diluted as it does so) all the way down to the 450 K potential temperature surface by March. Modeled tracer-tracer relationships evolve through the winter in a way similar to observations, but the separation between vortex and extravortex curves is exaggerated, suggesting that the model exhibits excessive horizontal mixing within and into the vortex. The tracer-tracer relationships are used to identify partly mixed air as lying, in tracer-tracer space, in a region intermediate between the characteristic vortex and midlatitude relationships. Air lying in a collar region just inside the vortex edge is thus identified as being mixed, and this indicates excessive horizontal mixing in the model across the vortex edge.