The current application of the zero discards policy in EU fisheries poses economic and logistic problems to fishing vessels, which are obliged to retain and preserve unwanted catches on board. The installation of compaction devices on board can effectively reduce the space requirements and the refrigeration loads to store these materials on board. In the current work, the performance of a pilot hydraulic press was optimized to attain a maximal volume reduction (i.e., maximal yield of press liquor) while keeping a reduced pollution load of the liquid effluents. To this end, a designed experiment was conducted where the yield (Y), the content of suspended solids (SS), and the chemical oxygen demand (COD) of the press liquor were related to the main operation parameters of the pilot plant (i.e., number of pressing steps and time of relaxation between consecutive steps). Statistical modeling, coupled to a multiobjective optimization technique (i.e., the weighted-sum method), was employed to find a set of optimal solutions meeting three objectives: maximal Y (i.e., maximal volume reduction of the press cake), and minimal SS and COD of the press waters. This approach concluded that 5 pressing steps and a time of relaxation between 105 and 120 s ensured a low content of SS (0.0170–0.0185 kg solids/kg sardine), while the yield was high (0.1942–0.2001 kg liquid/kg sardine) and COD remained below 24.4 g O2/kg sardine.