There is increasing interest in enabling positive experiences, not just minimizing negative experiences, to improve the welfare of farmed animals. This has influenced the growth of private agri-food standards and supported arguments to integrate animal welfare into policy on sustainability and climate change. However, much research finds that farmers predominantly focus on the minimization of negatives (i.e., health issues). This may impact the positioning of farmers within these wider societal debates, affecting their social license to farm. It is thus important to better understand farmers' priorities relating to the minimization of negative factors (e.g., health issues) and the promotion of positive experiences (i.e., natural behaviors). A novel 2 × 2 factorial survey using vignettes, which experimentally manipulated health (health issues minimized/not minimized) and natural behavior (natural behaviors promoted/not promoted) provision, was completed by livestock farmers (n = 169), mostly with extensive systems, in the UK and Republic of Ireland. The majority (88%) considered "minimizing health issues" to be the most important factor for animal well-being. However, the overall welfare of animals was judged to be highest when both health and natural behaviors were supported. Several individual characteristics, including farming sector, production system, gender, belief in animal mind and business type influenced how participants judged the welfare of animals and the level of importance they gave to health and natural behaviors. Findings suggest that although farmers prioritize the minimization of health issues they want animals to be both healthy and able to express natural behaviors, and individual characteristics are important for understanding farmers' welfare-related judgements.