In animals, including humans, free access to high-quality (generally energy-dense) food can result in obesity, leading to physiological and health problems. Consequently, various captive animals, including laboratory and companion animals and certain farm animals, are often kept on a restricted diet. Quantitative restriction of food is associated with signs of hunger such as increases in feeding motivation, activity and redirected oral behaviours which may develop into stereotypies. An alternative approach to energy intake restriction is to provide more food, but of a reduced quality. Such alternative diets are usually high in fibre and have lower energy density. The benefits of these alternative diets for animals are controversial: some authors argue that they result in more normal feeding behaviour, promote satiety and so improve animal welfare; others argue that [`]metabolic hunger' remains no matter how the restriction of energy intake and weight gain is achieved. We discuss the different arguments behind this controversy, focusing on two well-researched cases of food-restricted farmed livestock: pregnant sows and broiler breeders. Disagreement between experts results from differences in assumptions about what determines and controls feeding behaviour and food intake, from the methodology of assessing animal hunger and from the weighting placed on [`]naturalness' of behaviour as a determinant of welfare. Problems with commonly used behavioural and physiological measures of hunger are discussed. Future research into animal feeding preferences, in particular the relative weight placed on food quantity and quality, would be valuable, alongside more fundamental research into the changes in feeding physiology associated with alternative diets.