Fully connected push-based P2P overlay networks, such as P2PSP (P2P Straightforward Protocol), are an efficient alternative to tree-shaped overlay ones. In P2PSP, as in many other P2P systems, malicious peers (MPs) can perform collaborative pollution and free-riding attacks. Here, we summarize current solutions for these problems. We are not interested in make the content private but in mitigating the previous attacks. The proposed solution is based on Shamir's Secret Sharing (SSS) and the use of trusted peers (TPs). Under the assumption that the number of malicious peers is smaller than the half of the total, our proposal forces any peer to relay unpolluted content to well-intended peers in order to not to be expelled. We show the overhead added to the protocol, its strengths, its weaknesses, and outline possible solutions for these weakness.