The smooth transitions between turns in natural conversation suggest that speakers often begin to plan their utterances while listening to their interlocutor. The presented study investigates whether this is indeed the case and, if so, when utterance planning begins. Two hypotheses were contrasted: that speakers begin to plan their turn as soon as possible (in our experiments less than a second after the onset of the interlocutor’s turn), or that they do so close to the end of the interlocutor’s turn. Turn-taking was combined with a finger tapping task to measure variations in cognitive load. We assumed that the onset of speech planning in addition to listening would be accompanied by deterioration in tapping performance. Two picture description experiments were conducted. In both experiments there were three conditions: (1) Tapping and Speaking, where participants tapped a complex pattern while taking over turns from a pre-recorded speaker, (2) Tapping and Listening, where participants carried out the tapping task while overhearing two pre-recorded speakers, and (3) Speaking Only, where participants took over turns as in the Tapping and Speaking condition but without tapping. The experiments differed in the amount of tapping training the participants received at the beginning of the session. In Experiment 2, the participants’ eye-movements were recorded in addition to their speech and tapping. Analyses of the participants’ tapping performance and eye movements showed that they initiated the cognitively demanding aspects of speech planning only shortly before the end of the turn of the preceding speaker. We argue that this is a smart planning strategy, which may be the speakers’ default in many everyday situations.