There has been encouragement from funders, universities and academics to co-produce research. Co-production of research can be considered a methodology in its own right, or an underpinning set of principles for other methods. Co-production aims to reshape relations between the researched and the researcher. Yet, co-producing research rarely starts with a blank sheet, and is informed by antecedent power as well as prior experiences and expectations. Attention has been paid to practical barriers to co-production, such as time and resources, and there has been critical analysis of the claims made. The 'hidden politics' of co-production as a research approach have also been identified. This paper contributes to debates about such hidden politics of the co-production methodology in research. How leadership in research takes place matters, as it is a way of handling contestation over different aspects of methods, including the purpose and practices of research, and power differentials in co-production. This study was motivated by the experiences of the authors of a co-produced research project on participatory urban governance.