A burst is a large number of events occurring within a certain time window. As an unusual activity, it's a noteworthy phenomenon in many natural and social processes. Many data stream applications require the detection of bursts across a variety of window sizes. For example, stock traders may be interested in bursts having to do with institutional purchases or sales that are spread out over minutes or hours. Detecting a burst over any of k window sizes, a problem we call elastic burst detection, in a stream of length N naively requires O(kN) time. Previous work [24] showed that a simple Shifted Binary Tree structure can reduce this time substantially (in very favorable cases near to O(N)) by filtering away obvious non-bursts. Unfortunately, for certain data distributions, the filter marks many windows of events as possible bursts, even though a detailed check shows them to be non-bursts. In this paper, we present a new algorithmic framework for elastic burst detection: a family o...