Summary 1. Conflict management is a difficult problem in conservation biology. We worked with stakeholders to address the long-standing conflict arising from hen harrier Circus cyaneus predation on red grouse Lagopus lagopus. We modelled the impact of different harrier densities on grouse populations, which could be achieved through a quota system implemented by moving harriers once a threshold density has been reached. 2. We describe a stochastic population dynamics model for grouse populations in the presence of different densities of nesting harriers. The model was commissioned by, and the underlying principles and data sets agreed with, a stakeholder group representing a wide spectrum of conservation and moorland management interests. 3. Grouse populations commonly show cyclic dynamics. The stakeholder group identified the recovery phase from low grouse densities to a level at which driven shooting can recommence as being of paramount concern to the managers of grouse moors. 4. Parameter values used were informed using agreed data sets, allowing for uncertainty in parameter values as well as for temporal and spatial variation in demographic rates. Multiple runs of the model enabled us to construct probability distributions, both for the population sizes in the first two years following cyclic lows in the grouse populations and for the number of years to recommencement of driven grouse shooting. 5. The model results quantified the extent to which high densities of harriers pose challenges for grouse management. However, harrier impacts are relatively low at harrier densities of or below 0.025km2, suggesting that a quota scheme could theoretically support coexistence between grouse shooting and harrier conservation. 6. Synthesis and applications. Conflict management requires dialogue between conflicting parties, and can benefit from objective inputs from scientists using an agreed evidence base and transparent derivation of relevant information from that evidence base. By discussing the principles of model development and eligibility of data sets with a stakeholder group in advance of producing model results, we achieved buy-in from all parties involved. By developing a stochastic model allowing for variation and uncertainty, we have informed the debate in as objective manner as possible: whether this additional information will lead to the development and testing of a quota system being taken up in practice remains to be seen.