The Southern Hemisphere winter stratosphere exhibits prominent traveling planetary-scale Rossby waves, which generally are not able to induce Stratospheric Sudden Warmings. A series of runs of a simplified general circulation model is presented, aimed at better understanding the generation of these waves. While the generation of planetary-scale traveling waves through the interaction of synoptic-scale waves is observed in a control run, when the model is truncated to permit only waves with zonal wave number 1 or 2, the long waves are found to increase in strength, leading to a considerably more active stratosphere including Sudden Warmings comparable in strength to Northern Hemisphere winter. This finding suggests that the role of tropospheric synoptic eddies is two-fold: while generating a weak planetary-scale wave flux into the stratosphere, their main effect is to suppress baroclinic instability of planetary-scale waves by stabilizing the tropospheric mean state.