This paper presents an application of a new methodological framework for undertaking distributional cost-effectiveness analysis to combine the objectives of maximising health and minimising unfair variation in health when evaluating population health interventions. The National Health Service bowel cancer screening programme introduced in 2006 is expected to improve population health on average and to worsen population health inequalities associated with deprivation and ethnicity – a classic case of ‘intervention-generated inequality’. We demonstrate the distributional cost-effectiveness analysis framework by examining two redesign options for the bowel cancer screening programme: (i) the introduction of an enhanced targeted reminder aimed at increasing screening uptake in deprived and ethnically diverse neighbourhoods and (ii) the introduction of a basic universal reminder aimed at increasing screening uptake across the whole population. Our analysis indicates that the universal reminder is the strategy that maximises population health, while the targeted reminder is the screening strategy that minimises unfair variation in health. The framework is used to demonstrate how these two objectives can be traded off against each other, and how alternative social value judgements influence the assessment of which strategy is best, including judgements about which dimensions of health variation are considered unfair and judgements about societal levels of inequality aversion. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.