Fisheries management must address multiple, often conflicting objectives in a highly uncertain context. While the bio-economic performance of trawl fisheries faces high levels of biological and economic uncertainty, the impact of trawling on broader biodiversity is also a major concern for their management. The purpose of this study is to propose a model-based framework to formally assess the trade-offs associated with balancing biological, economic and non-target species conservation objectives in a mixed fishery. This framework is applied to the Australian Northern Prawn Fishery (NPF). We apply a stochastic co-viability framework of analysis to a multi-species bio-economic model of the NPF considering multiple management objectives. In particular, we consider the implications of including a formal non-target species conservation constraint. Results show that, due to the variability in the interactions between the fishery and the ecosystem, current management strategies present biological and economic risks. The trade-offs associated with respecting at each point in time biological, economic and non-target species conservation constraints with high probability and maximizing the net present value of the fishery are quantified.