Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problemsthat involve human health. Tree-based methods have been widely adopted for survival analysis due to their appealing interpretablility and their ability to capture complex relationships. However, most existing methods to produce survival trees rely on heuristic (or greedy) algorithms, which risk producing sub-optimal models. We present a dynamic-programming-with-bounds approach that finds provably-optimal sparse survival tree models, frequently in only a few seconds.