Business process optimization typically involves discovering models that are fit, precise, sound and simple. Process discovery algorithms automatically obtain these models from event logs, records of past process executions, enabling insights into the underlying process. However, event logs often contain incomplete and infrequent behaviour, which presents significant challenges for these algorithms. To address these issues, we propose a new process discovery technique called OptIMIIst, which guarantees soundness while handling both infrequent and incomplete behaviour and discovering locally optimal process trees. This technique, based on the Inductive Miner framework, operates in two steps. First, it creates candidate mining decisions for each process tree operator and then decides on the optimal decision through a local fitness and precision estimation. An experimental evaluation demonstrates that OptIMIIst produces high-quality process models and offers competitive fitness, precision, and simplicity compared to state-of-the-art techniques, while maintaining soundness.