We propose a scheme to reduce the overhead associated with channel state information (CSI) feedback required for opportunistic scheduling in wireless access networks. We study the case where CSI is partially overheard by mobiles and thus one can suppress transmitting CSI reports for time varying channels of inferior quality. We model the mechanism of feedback suppression as a Bayesian network, and show that the problem of minimizing the average feedback overhead is NP-hard. To deal with hardness of the problem we identify a class of feedback suppression structures which allow efficient computation of the cost. Leveraging such structures we propose an algorithm which not only captures the essence of seemingly complex overhearing relations among mobiles, but also provides a simple estimate of the cost incurred by a suppression structure. Simulation results are provided to demonstrate the improvements offered by the proposed scheme, e.g., a savings of 63-83% depending on the network size.