Advertising new information to users via push is the trigger of operation for many contemporary information systems. Furthermore, passive optical networks are expected to extend the reachability of high-quality push services to thousands of clients. The efficiency of a push service is the ratio of successfully informed users. However, pushing only data of high popularity can degrade the thematic coherency of the content. The present work offers a novel, analysis-derived, tunable way for selecting data for push services. The proposed scheme can maximize the service ratio of a push system with regard to data coherence constraints. Extensive simulations demonstrate the efficiency of the scheme compared to alternative solutions. The proposed scheme is the first to tackle the problem of data coherence-aware, service ratio optimization of push services.