Decision trees are a widely used family of methods for learning predictive models from both batch and streaming data. Despite depicting positive results in a multitude of applications, incremental decision trees continuously grow in terms of nodes as new data becomes available, i.e., they eventually split on all features available, and also multiple times using the same feature, thus leading to unnecessary complexity and overfitting. With this behavior, incremental trees lose the ability to generalize well, be human-understandable, and be computationally efficient. To tackle these issues, we proposed in a previous study a regularization scheme for Hoeffding decision trees that (i) uses a penalty factor to control the gain obtained by creating a new split node using a feature that has not been used thus far and (ii) uses information from previous splits in the current branch to determine whether the gain observed indeed justifies a new split. In this paper, we extend this analysis and apply the proposed regularization scheme to other types of incremental decision trees and report the results in both synthetic and real-world scenarios. The main interest is to verify whether and how the proposed regularization scheme affects the different types of incremental trees. Results show that in addition to the original Hoeffding Tree, the Adaptive Random Forest also benefits from regularization, yet, McDiarmid Trees and Extremely Fast Decision Trees observe declines in accuracy.