This study investigated whether speakers strategically decide where to interrupt their speech once they need to stop. We conducted four naming experiments in which pictures of colored shapes occasionally changed in color or shape. Participants then merely had to stop (Experiment 1); or they had to stop and resume speech (Experiments 2-4). They were asked either to produce a simple noun phrase (Experiments 1-2 and 4) or a sentence structure in which the word order was reversed (Experiment 3). The task was performed in a non-communicative situation (Experiments 1-3) or in the presence of an interlocutor who needed to understand the utterance (Experiment 4). In all experiments, the time interval (SOA) between the initial and changed picture was varied, and the locus of word-internal interruptions (within color or shape word) depended on this SOA. In contrast to the predictions of Levelt (1983), people stopped both within correct and incorrect words. The proportions of word-internal interruptions and word completions were, however, influenced by the task instructions (e.g., there were more word completions and fewer word-internal interruptions when people resumed speech than when they did not). The results suggest that people sometimes decide to postpone their interruptions and complete their words instead of interrupting as fast as possible. We propose an account of speech interruption that includes strategic stopping.