Distilled sensing is a multistage active learning procedure to detect events scattered across sites. We assume that at each stage the number of sites that can be measured is fixed and focus on the question of the optimal distribution of measurements across sites. By defining a Bayesian objective based on maximising the expected number of detections we are able to efficiently compute the optimal measurement strategy at each stage by solving a knapsack problem. The procedure has potential application across the sciences in which one wishes to detect objects on the basis of a sequence of measurements.