Decision trees are commonly used structures in scenarios where explainable Machine Learning models are desired, as they are visually intuitive. In the existing literature, the search for explainability in trees involves minimizing metrics such as depth and number of nodes. In this context, we define an explainability metric, called explanation size, which reflects the number of attributes needed to explain the classification of examples. We also present an algorithm, called SER-DT, which obtains an O(log n) approximation (optimal if P different NP) for the minimization of depth in the worst/average case, as well as of explanation size in the worst/average case. In a series of experiments, we compared the SER-DT implementation with well-known algorithms in the field, such as CART and EC2 in addition to testing the impact of parameters and pruning strategies on these algorithms. SER-DT proved to be competitive in terms of accuracy with the aforementioned algorithms, but generated much more explainable trees.