The stability of realistic jets is examined in a linearized barotropic model on a sphere. Approximately nondispersive modes associated with a region of negative basic state absolute vorticity gradient on the poleward side of the jet are examined in detail. As in previous studies, broader jets and those which peak at higher latitudes produce poleward modes that are less dispersive. Jet profiles derived from observational data at 10, 5, and 2mb for three Southern Hemisphere winter months are used in the model, and the results are compared with quasi-nondispersive features (QNDF) which have been observed in satellite data in the Southern Hemisphere winter stratosphere. Characteristics of the barotropically unstable modes compare remarkably well with those of the observed modes. The barotropic model results for a month in which these features are not observed indicate the presence equatorward modes at wavenumbers 3 and 4 which grow considerably faster than the quasi-nondispersive poleward modes. We also note the appearance of westward moving modes in the summer hemisphere during June, and in analytical profiles with a realistic global structure.