Since laisser-faire managements has brought several fish stocks to collapse there is a need for developing sustainable harvesting methods which account for ecosystem services, beyond yield, such as conservation of fish stocks. We provide the solution through a multi-objective fishing strategy approach. Using a stage-structured population model by De Roos et al with stage-selective harvesting and the concept of recovery potential, we demonstrate that fishing for maximum sustainable yield can bring the population dangerously close to extinction. We use Pareto frontiers to find preferable alternative harvesting strategies that provide superior conservational benefits, such as reduced risk of extinction, for only a small reduction in yield. Moreover, we demonstrate that the impact of fishing on the size-structure of the population is a good proxy for assessing the risk of extinction. To ensure robustness of our results we rigorously prove the existence of at most one positive steady state, and numerical investigations of the basin of attraction suggest that this steady state is globally stable when it exists. We also repeat our simulated results for a large set of parameter values.