The problem of state space search is fundamental to many areas of computer science, such as, e.g., AI and formal methods. Often, the state space to be searched is huge, so optimizing the search is an important issue. In this paper, we consider the problem of visiting all states in the setting where transitions between states are generated by actions, and the (reachable) states are not known in advance. Some of the actions may commute, i.e., they result in the same state for every order in which they are taken. We show how to use commutativity to achieve full coverage of the states, while traversing a relatively small number of edges.