A new dispersion relation, and associated stability criteria, is derived for low-n external kink and infernal modes, and is applied to modelling the stability properties of quiescent H-mode like regimes. The analysis, performed in toroidal geometry with large edge pressure gradients associated with a local flattening of the safety factor, includes a pedestal, sheared toroidal rotation and a vacuum region separating the plasma from an ideal metallic wall. The external kink-infernal modes found here exhibit similarities with experimentally observed edge harmonic oscillations.