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Work on decentralized discrete-event control systems is extended to handle the case when, instead of always observing or never observing an event, a supervisor may observe only some occurrences of a particular event. Results include a necessary and sufficient condition for solving this version of the decentralized problem (which is analogous to the co-observability property used in the standard version of the problem) and a method for checking when this condition holds. In this paper, whether an event is observed by a given agent is dependent on that agent's state (or the string of events that agent has seen so far). This model of event observation is applicable to problems where a supervisor communicates observations of event occurrences to another supervisor to help the other one make control decisions.