Large language models (LLMs) are increasingly integrated into complex software systems, raising critical security and privacy concerns. Imagine sensitive data from one part of a system influencing an LLM's behavior in another, potentially leaking confidential information or spreading corrupted data. Researchers are tackling this challenge with dynamic information flow tracking, a method of labeling data by its sensitivity (e.g., "trusted" vs. "untrusted"). However, simply labeling the LLM's output with the most restrictive label of its inputs is too rigid. This new research introduces a more nuanced method called *permissive information-flow analysis*. Instead of assuming all inputs influence the LLM equally, this method identifies only the *truly influential* inputs. It then applies the appropriate label based on those influential data points. This approach is like a detective carefully tracing the real sources of information rather than making broad assumptions. This approach is tested using two techniques: 1) enhancing the prompt given to an LLM with retrieved documents (RAG) and 2) a k-Nearest-Neighbor Language Model (kNN-LM). Initial findings are promising, particularly in the case of RAG. These findings suggest that permissive label propagation is a practical way to manage information flow in LLM systems, improving the potential for these models to be used more broadly, all while keeping our secrets safe.