We use a linear quasi-geostrophic &bgr;-plane model to study large-scale instabilities of the Jovian upper troposphere forced from below by zonal jets. The jets are presumed to be barotropically stable in the isentropic deep interior, but barotropically unstable in the statically stable upper troposphere. We explore the effect on this barotropic instability of weak vertical shear causing the jets to decay with height and find: (1) eastward jets are stabilized by weaker shear than westward jets. (2) the most unstable eddies are strongly confined by the shear, (3) eddy fluxes contribute to vertical decay of the jets, (4) the lower residual mean meridional circulation cells exhibit rising motion in regions of anticyclonic shear, but these are overlain by reverse cells. ¿ American Geophysical Union 1989