Alignment of the 87 available sequences of group I self-splicing introns reveals numerous instances of covariation between distant sites. Some of these covariations cannot be ascribed to historical coincidences or the known secondary structure of group I introns, and are, therefore, best explained as reflecting tertiary contacts. With the help of stereochemical modelling, we have taken advantage of these novel interactions to derive a three-dimensional model of the conserved core of group I introns. Two noteworthy features of that model are its extreme compactness and the fact that all of the most evolutionarily conserved residues happen to converge around the two helices that constitute the substrate of the core ribozyme and the site that binds the guanosine cofactor necessary for self-splicing. Specific functional implications are discussed, both with regard to the way the substrate helices are recognized by the core and possible rearrangements of the introns during the self-splicing process. Concerning potential long-range interactions, emphasis is put on the possible recognition of two consecutive purines in the minor groove of a helix by a GAAA or related terminal loop.