Recently, in June, our group submitted a new proposal, namely FAEST, to the current NIST PQ signature (additional round) competition. By taking advantage of a new proof system (QuickSilver) based on VOLE-in-the-Head (Vector Linear Oblivious Evaluation), FAEST allows a significant decrease in both signature size and sign/verify time when compared to the state of the art MPC-in-the-Head designs. Currently, we are exploring other possible ways one can further improve the FAEST performance. In my talk, I will be presenting one of the optimization ideas, namely, what role does a one-way-function play when determining the performance of FAEST or any other MPCitH based signature scheme, and can one use it to their advantage?