We present a general-purpose, loss less compressor for streaming data. This compressor is based on the deplump probabilistic compressor for batch data. Approximations to the inference procedure used in the probabilistic model underpinning deplump are introduced that yield the computational asyptotics necessary for stream compression. We demonstrate the performance of this streaming deplump variant relative to the batch compressor on a benchmark corpus and find that it performs equivalently well despite these approximations. We also explore the performance of the streaming variant on corpora that are too large to be compressed by batch deplump and demonstrate excellent compression performance.