The Very Fast Decision Tree (VFDT) is one of the most important classification algorithms for real-time data stream mining. However, imperfections in data streams, such as noise and imbalanced class distribution, do exist in real world applications and they jeopardize the performance of VFDT. Traditional sampling techniques and post-pruning may be impractical for a non-stopping data stream. To deal with the adverse effects of imperfect data streams, we have invented an incremental optimization model that can be integrated into the decision tree model for data stream classification. It is called the Incrementally Optimized Very Fast Decision Tree (I-OVFDT) and it balances performance (in relation to prediction accuracy, tree size and learning time) and diminishes error and tree size dynamically. Furthermore, two new Functional Tree Leaf strategies are extended for I-OVFDT that result in superior performance compared to VFDT and its variant algorithms. Our new model works especially well for imperfect data streams. I-OVFDT is an anytime algorithm that can be integrated into those existing VFDT-extended algorithms based on Hoeffding bound in node splitting. The experimental results show that I-OVFDT has higher accuracy and more compact tree size than other existing data stream classification methods.