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We describe an approach to elastically scale the performance of a data analytics operator that is part of a streaming application. Our techniques focus on dynamically adjusting the amount of computation an operator can carry out in response to changes in incoming workload and the availability of processing cycles. We show that our elastic approach is beneficial in light of the dynamic aspects of streaming workloads and stream processing environments. Addressing another recent trend, we show the importance of our approach as a means to providing computational elasticity in multicore processor-based environments such that operators can automatically find their best operating point. Finally, we present experiments driven by synthetic workloads, showing the space where the optimizing efforts are most beneficial and a radioastronomy imaging application, where we observe substantial improvements in its performance-critical section.