Large Language Models in Conversation-Based Assessment tend to provide inappropriate hints that compromise validity. We demonstrate that self-critique – a simple prompt engineering technique – effectively constrains this behavior.Through two studies using synthetic conversations and real-world high school math pilot data, self-critique reduced inappropriate hints by 90.7% and 24-75% respectively. Human experts validated ground truth labels while LLM judges enabled scale. This immediately deployable solution addresses the critical tension in intermediate-stakes assessment: maintaining student engagement while ensuring fair comparisons. Our findings show prompt engineering can meaningfully safeguard assessment integrity without model fine-tuning.