The problem of minimizing communication of event occurrences in systems modeled by finite-state automata is considered. There are n communicating agents observing the behavior of the system for purposes of control or diagnosis. A set of communication policies for the agents is said to be minimal if communications of event occurrences cannot be removed without affecting the correctness of the solution. Under an assumption on the absence of cycles (other than self-loops) in the system model, an algorithm that computes a set of minimal communication policies in polynomial time in the number of states of the system is presented.