Sustainable consumption aims to minimize the environmental and societal impact of the use of services and products. Over-consumption of services and products leads to potential natural resource exhaustion and societal inequalities as access to goods and services becomes more challenging. In everyday life, a person can simply achieve more sustainable purchases by drastically changing their lifestyle choices and potentially going against their personal values or wishes. Conversely, achieving sustainable consumption while accounting for personal values is a more complex task as potential trade-offs arise when trying to satisfy environmental and personal goals. This article focuses on value-sensitive design of recommender systems, which enable consumers to improve the sustainability of their purchases while respecting personal and societal values. Value-sensitive recommendations for sustainable consumption are formalized as a multi-objective optimization problem, where each objective represents different sustainability goals and personal values. Novel and existing multi-objective algorithms calculate solutions to this problem. The solutions are proposed as personalized sustainable basket recommendations to consumers. These recommendations are evaluated on a synthetic dataset, which comprises three established real-world datasets from relevant scientific and organizational reports. The synthetic dataset contains quantitative data on product prices, nutritional values, and environmental impact metrics, such as greenhouse gas emissions and water footprint. The recommended baskets are highly similar to consumer purchased baskets and aligned with both sustainability goals and personal values relevant to health, expenditure, and taste. Even when consumers would accept only a fraction of recommendations, a considerable reduction of environmental impact is observed.