The geometry of crescent-shaped noble-metal nanoparticles is systematically varied in terms of shape and size. The resulting changes in the plasmonic resonances of these structures are investigated by extinction spectroscopy revealing a rich polarization-dependent response in the near- infrared region of the electromagnetic spectrum. A first approach towards the understanding of this behaviour, in analogy to previous models on confined modes in nanometric metal slabs, is presented and discussed. Variations in several geometrical parameters lead to changes in the optical response that can be understood within this model. Qualitative changes in the response are seen at the transition of the structures from an open ‘crescent’ to a fully connected ring, pointing to a high field localization between the two tips of the structure.