The development of a range of convoluted elements derived from linear and crossed dipoles is traced and their performance is examined experimentally and analytically in relation to their application to frequency-selective surfaces. These configurations give highly packed structures for use on curved surfaces or where maximum separation from the onset of grating responses is required. Two potential methods of analysis are a Floquet modal approach and a spectral iteration. Current distributions on an illustrative example are given. Calculated transmission responses of a convoluted dipole containing three cycles agree well with experiment.