In security games, the solution concept commonly used is that of a Stackelberg equilibrium where the defender gets to commit to a mixed strategy. The motivation for this is that the attacker can repeatedly observe the defender's actions and learn her distribution over actions, before acting himself. If the actions were not observable, Nash (or perhaps correlated) equilibrium would arguably be a more natural solution concept. But what if some, but not all, aspects of the defender's actions are observable? In this paper, we introduce solution concepts corresponding to this case, both with and without correlation. We study their basic properties, whether these solutions can be efficiently computed, and the impact of additional observability on the utility obtained.