We investigate the label complexity of active learning under some smoothness assumptions on the data-generating process.We propose a procedure, PLAL, for “activising” passive, sample-based learners. The procedure takes an unlabeledsample, queries the labels of some of its members, and outputs a full labeling of that sample. Assuming the data satisfies “Probabilistic Lipschitzness”, a notion of clusterability, we show that for several common learning paradigms, applying our procedure as a preprocessing leads to provable label complexity reductions (over any “passive”learning algorithm, under the same data assumptions). Our labeling procedure is simple and easy to implement. We complement our theoretical findings with experimental validations.