In the context of a data stream, a classifier must be able to learn from a theoretically-infinite stream of examples using limited time and memory, while being able to predict at any point. Many methods deal with this problem by basing their model on a window of examples. We introduce a probabilistic adaptive window (PAW) for data-stream learning, which improves this windowing technique with a mechanism to include older examples as well as the most recent ones, thus maintaining information on past concept drifts while being able to adapt quickly to new ones. We exemplify PAW with lazy learning methods in two variations: one to handle concept drift explicitly, and the other to add classifier diversity using an ensemble. Along with the standard measures of accuracy and time and memory use, we compare classifiers against state-of-the-art classifiers from the data-stream literature.