Adults ask children questions in a variety of contexts, for example, in the classroom, in the forensic context, or in experimental research. In such situations children will inevitably be asked some questions to which they do not know the answer, because they do not have the required information (“unanswerable” questions). When asked unanswerable questions, it is important that children indicate that they do not have the required information to provide an answer. These 2 studies investigated whether preinterview instructions (Experiment 1) or establishing a memory narrative (Experiment 2) helped children correctly indicate a lack of knowledge to unanswerable questions. In both studies, 6- and 8-year-olds participated in a classroom-based event about which they were subsequently interviewed. Some of the questions were answerable, and some were unanswerable. Results showed that preinterview instructions increased the number of younger children's appropriate “don't know” responses to unanswerable questions, without decreasing correct responses to answerable questions. This suggests that demand characteristics affect children's tendency correctly to say “I don't know.” The opportunity to provide a narrative account increased children's appropriate “don't know” responses to unanswerable yes/no questions, and increased the number of younger children's correct responses to answerable questions. This suggests that cognitive factors also contribute to children's tendency correctly to say “I don't know.” These results have implications for any context where adults need to obtain information from children through questioning, for example, a health practitioner asking about a medical condition, in classroom discourse, in the investigative interview, and in developmental psychology research.