Speech planning is a sophisticated process. In dialog, it regularly starts in overlap with an incoming turn by a conversation partner. We show that planning spoken responses in overlap with incoming turns is associated with higher processing load than planning in silence. In a dialogic experiment, participants took turns with a confederate describing lists of objects. The confederate's utterances (to which participants responded) were pre-recorded and varied in whether they ended in a verb or an object noun and whether this ending was predictable or not. We found that response planning in overlap with sentence-final verbs evokes larger task-evoked pupillary responses, while end predictability had no effect. This finding indicates that planning in overlap leads to higher processing load for next speakers in dialog and that next speakers do not proactively modulate the time course of their response planning based on their predictions of turn endings. The turn-taking system exerts pressure on the language processing system by pushing speakers to plan in overlap despite the ensuing increase in processing load.