Many applications use classification models on streaming data to detect actionable alerts. Due to concept drifts in the underlying data, how to maintain a model?s up-to-dateness has become one of the most challenging tasks in mining data streams. State of the art approaches, including both the incrementally updated classifiers and the ensemble classifiers, have proved that model update is a very costly process. In this paper, we introduce the concept of model granularity. We show that reducing model granularity will reduce model update cost. Indeed, models of fine granularity enable us to efficiently pinpoint local components in the model that are affected by the concept drift. It also enables us to derive new components that can easily integrate with the model to reflect the current data distribution, thus avoiding expensive updates on a global scale. Experiments on real and synthetic data show that our approach is able to maintain good prediction accuracy at a fraction of model updating cost of state of the art approaches.