Analytical and numerical results are presented that demonstrate the destabilizing effect of pressure gradients at the plasma edge of a thin-shell RFP. Asymptotic solutions of the marginal MHD equation are used to derive stability criteria for modes resonant close to either side of the resistive wall. These are shown to be consistent with criteria derived from the energy principle, and suggest that modes just nonresonant at the plasma boundary are destabilized. Numerical integration of the marginal MHD equation, for a finite-beta profile, confirms this modification of the m=1 spectrum. The resulting pressure-driven instabilities are offered as an explanation for the n=(9, 10, 11) modes observed in the m=1 spectrum of HBTX1C.