When telling a story, a speaker needs to refer to story characters using appropriate expressions, which requires a mental model of the discourse. We hypothesize that, compared to those of adults, children's discourse models are based more on factors that are less cognitively demanding, such as animacy, and as they grow older, discourse factors such as givenness will start to play a larger role. To test this, we conducted a longitudinal study of referring expression use in elicited narratives. Swedish-speaking children (n = 17) were tested three times between age 4 and 7 and compared to adults (n = 20). The results show that children, like adults, take into account if, when and how a character has been mentioned earlier when referring, but that they rely more on animacy than adults. These results indicate that the various cues for referential choices are in place in preschool children's discourse models, but are weighted differently than in adults.