Context Invasive non-native species are on the rise worldwide, exacerbating already significant environmental and economic impacts. Concurrently, public attitudes towards methods of controlling these species are changing, with greater demand for non-lethal solutions. This has fostered research into developing new, effective technologies and strategies for wildlife management. Aims On the basis of a case study focusing on the eastern grey squirrel (Sciurus carolinensis) in the UK, this study aimed to understand the potential for population management, using either live trapping or oral contraception. First, assuming completely coordinated landscape-scale control, and then, coordinated control only on parts of the landscape, accounting for the potential that landowners’ attitudes towards alternative methods may differ and reflect those of the wider public. Methods We used an existing spatially explicit individual-based modelling approach applying various parameterisations to define management. We varied the density of traps or hoppers delivering contraceptives, the duration of deployment, contraceptive efficacy, initial population size, and the probability of landowner participation. The latter was based on a previous public survey, suggesting that 40% of the respondents were open to management using trapping and 64% to using contraception. Key results With complete coordinated control, trapping was generally faster and more cost-effective than was contraception. However, when differences in social acceptance were considered, reducing participation and, consequently, the spatial coverage of management, contraception was found to maintain greater population reductions than was trapping with similar effort, assuming a contraceptive efficacy of 75% or higher. Conclusions This study added another layer of complexity to managing invasive non-native species, namely the potential effect that landowners’ attitudes to different methods of population management might have on the level of coordinated control at landscape scale. In a situation such as the one modelled by this study, where management is not a legal requirement, this human dimension must be considered alongside cost-effectiveness, to develop successful control in line with management goals. Implications Further work is required to establish the actual attitudes of landowners, and in different contexts (e.g. urban, rural areas), how this may change as new approaches become available, and then how spatial variation (clustering) in the resulting wildlife population control may affect outcomes.