Many important systems feature strongly curved interfaces with low surface tension. Four examples are micelles, emulsions, giant bilayer vesicles, and biological membranes. A fifth is the microbubble nuclei that initiate cavitation in aqueous media. A model describing these nuclei and how they respond to changes in ambient pressure attributes their remarkable resiliency to a surrounding film of surface-active molecules, An independent derivation of this model is obtained in this paper by applying thermodynamic methods formulated recently to describe strongly curved amphiphilic interfaces. This illuminates previous models for microbubble nuclei and provides additional information on the mechanical and thermodynamic properties of interfaces in general.