Sustainable diets incorporate consumer acceptability whilst being nutritious and having a low carbon footprint. This paper estimated Exact Affine Stone Index (EASI) incomplete demand systems for different households using the Scottish section of Kantar Worldpanel data from 2010 to 2015. The resulting price elasticities were used within the Green et al (2015) quadratic programming diet model to estimate the quantities of food products which would constitute a sustainable diet. Four demographic groups were modelled and the results suggested that three of the groups could experience carbon emission reductions of between 30 to 55 per cent relative to baseline emissions. The diets would also likely offer an improvement in terms of nutritional quality as measured by the Mean Excess Ratio (MER).