A burst is a large number of events occurring within a certain time window. 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. In this paper, we present a new algorithmic framework for elastic burst detection : a family of data structures that generalizes the Shifted Binary Tree, and a heuristic search algorithm to find an efficient structure given the input. We study how different inputs affect the desired structures and the probability to trigger a detailed search. Experiments on both synthetic and real world data show a factor of up to 35 times improvement compared with the Shifted Binary Tree over a wide variety of inputs, depending on the inputs.