Previous research shows that posing many questions about an event may lead to asking questions about unwitnessed details and that people sometimes provide substantive and erroneous answers to them. Therefore, two experiments investigated the role of the problem-solving and judgment processes, which are unrelated to memory access, in improving responding to unanswerable questions. Experiment 1 compared the effects of a brief retrieval training with the effects of an instruction to increase the criterion of reporting. As expected, the two manipulations had different effects on participants' answers, which demonstrates that training can do more than just instigate more cautious responding. However, we found evidence against our prediction that an enhancement in metacognitive ability underlies improved responding after training. Experiment 2 investigated, for the first time, the role of constant awareness that questions can be unanswerable and that such questions should be rejected. We compared the effects of training with the effects of a small change in response format that ensured such awareness. The effects of the two manipulations were similar, which supports our prediction that the constant awareness of unanswerable questions is a key factor behind improved responding. Practical implications for the eyewitness memory domain are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).