It has been suggested that a referent’s accessibility is affected by the degree to which it is in the speaker’s attention. Assuming that less accessible referents are less likely to be pronominalized, this predicts that speakers under cognitive load use more elaborate referring expressions. However, speakers under load may also have difficulty taking into account their addressee’s perspective, which may either lead to more use of the speaker’s own discourse model or to more economic expressions. To tease these effects apart, we conducted a story completion experiment in which cognitive load was manipulated by the presence or absence of a secondary task for the speaker. In addition, we dissociated the speaker’s and the addressee’s perspectives. Our results do not provide evidence for the hypothesis that cognitive load reduces the accessibility of referents in the speaker’s own discourse model, suggesting that speaker attention does not determine accessibility.