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Previous studies have found that the most consistent response of the eddy-driven jet to sea ice loss and Arctic amplification in fully coupled general circulation models (GCMs) is a broad region of anomalous easterlies on the poleward flank. In this study, a similar response is noted in a dry dynamical core GCM with imposed surface heating at the pole, and it is shown that in both a fully coupled GCM's North Atlantic basin and the dry dynamical core, the anomalous easterlies cause an asymmetrical narrowing of the jet on the poleward flank of the climatological jet. A suite of barotropic model simulations run with polar forcing shows decreased jet positional variability consistent with a narrowing of the jet profile, and it is proposed that this narrowing decreases the distance Rossby waves can propagate away from the jet core, which drives changes in jet variability. Since Rossby wave propagation and dissipation is intrinsic to the development and maintenance of the eddy-driven jet, and is tightly coupled to a jet's variability, this acts as a meridional constraint on waves' ability to propagate outside of the jet core, leading to the decreased variability in zonal-mean jet position. The results from all three models demonstrates that this relationship is present across a model hierarchy.