Conversational Recommendation Systems (CRSs) are a particularly interesting application for out-of-the-box LLMs due to their potential for eliciting user preferences and making recommendations in natural language across a wide set of domains. Somewhat surprisingly, we find however that in such a conversational application, the more questions a user answers about their preferences, the worse the model’s recommendations become. We demonstrate this phenomenon on a previously published dataset as well as two novel datasets which we contribute. We also explain why earlier benchmarks failed to detect this round-over-round performance loss, highlighting the importance of the evaluation strategy we use and expanding upon Li et al. (2023a). We also present preference elicitation and recommendation strategies that mitigate this degradation in performance, beating stateof-the-art results, and show how three underlying models, GPT-3.5, GPT-4, and Claude 3.5 Sonnet, differently impact these strategies. Our datasets and code are available at https://github.com/CtrlVGustavo/A-Flashin-the-Pan-CRS.