Process mining techniques are able to extract knowledge from event logs commonly available in today’s information systems. These techniques provide new means to discover, monitor, and improve processes in a variety of application domains. Process discovery—discovering a process model from example behavior recorded in an event log—is one of the most challenging tasks in process mining. A variety of process discovery techniques have been proposed. Most techniques suffer from the problem that often the discovered model is internally inconsistent (i.e., the model has deadlocks, livelocks or other behavioral anomalies). This suggests that the search space should be limited to sound models. In this paper, we propose a tree representation that ensures soundness. We evaluate the impact of the search space reduction by implementing a simple genetic algorithm that discovers such process trees. Although the result can be translated to conventional languages, we ensure the internal consistency of the resulting model while mining, thus reducing the search space and allowing for more efficient algorithms.