Very Fast Decision Tree (VFDT) is one of the most popular decision tree algorithms in data stream mining. The tree building process is based on the principle of the Hoeffding bound to decide on splitting nodes with sufficient data statistics at the leaf. The original version of VFDT requires a user-defined tie threshold by which a split will be forced to break to control the tree size. It is an open problem that the tree size grows tremendously with noise as continuous data stream in and the classifier's accuracy drops. In this paper, we propose a Moderated VFDT (M-VFDT), which uses an adaptive tie threshold for node splitting control by incremental computing. The tree building process is as fast as that of the original VFDT. The accuracy of M-VFDT improves significantly even under the presence of noise in the data stream. To solve the explosion of tree size, which is still an inherent problem in VFDT, we propose two lightweight pre-pruning mechanisms for stream mining (post-pruning is not appropriate here because of the streaming operation). Experiments are conducted to verify the merits of our new methods. M-VFDT with a pruning mechanism shows a better performance than the original VFDT at all times. Our contribution is a new model that can efficiently achieve a compact decision tree and good accuracy as an optimal balance in data stream mining.