Despeckling techniques based on the nonlocal approach provide an excellent performance, but exhibit also a remarkable complexity, unsuited to time-critical applications. In this letter, we propose a fast nonlocal despeckling filter. Starting from the recent SAR-BM3D algorithm, we propose to use a variable-size search area driven by the activity level of each patch, and a probabilistic early termination approach that exploits speckle statistics in order to speed up block matching. Finally, the use of look-up tables helps in further reducing the processing costs. The technique proposed conjugates excellent performance and low complexity, as demonstrated on both simulated and real-world SAR images and on a dedicated SAR despeckling benchmark.