The definitions of the basic concepts, rules, and constraints of centering theory involve underspecified notions such as `previous utterance', `realization', and `ranking'. We attempted to find the best way of defining each such notion among those that can be annotated reliably, and using a corpus of texts in two domains of practical interest. Our main result is that trying to reduce the number of utterances without a backwardlooking center (CB) results in an increased number of cases in which some discourse entity, but not the CB, gets pronominalized, and viceversa. 1 MOTIVATION Centering Theory (Grosz et al., 1995; Walker et al., 1998b) is best characterized as a `parametric' theory: its key definitions and claims involve notions such as `utterance', `realization', and `ranking' which are not completely specified; their precise definition is left as a matter for empirical research, and may vary from language to language. A first goal of the work pr...