We investigated whether speakers use more redundant descriptions for listeners under increased cognitive load. We conducted a referential communication experiment in a driving simulator, predicting that speakers would be more redundant when listeners perform a difficult as compared to an easy driving task. The results confirmed this prediction, but only when the speaker had previously taken the role of driver, and only in the first block of the experiment. These findings suggest that speakers only take the listener’s needs into account when there are strong cues that adaptation is necessary, and only adapt to their first assessment of listeners' needs.