One knowledge discovery problem in the rapid response setting is the cost of learning which patterns are indicative of a threat. This typically involves a detailed follow-through, such as review of documents and information by a skilled analyst, or detailed examination of a vehicle at a border crossing point, in deciding which suspicious vehicles require investigation. Assessing various strategies and decision rules means we must compare not only the short term effectiveness of interrupting a specific traveler, or forwarding a specific document to an analyst, but we must also weigh the potential improvement in our profiles that results even from sending a "false alarm". We show that this problem can be recast as a dynamic programming problem with, unfortunately, a huge state space. Several specific heuristics are introduced to provide improved approximations to the solution. The problems of obtaining real-world data to sharpen the analysis are discussed briefly.