Objective: To determine the types and proportions of vegetable oils to recommend for a healthy diet. Methods: Optimal vegetable oil combinations were designed, using linear programming and, as decision variables, nine single oils and 29 basic food items. ‘Oil models’ were run to determine whether reasonable amounts of individuals oils or oil mixtures satisfied a set of constraints on essential fatty acids and vitamin E. ‘Meal models’ were run to test whether selected mixtures could be used as the sole source of added fat in a meal that met micronutrient and macronutrient recommendations. Results: The cheapest mixture (0.97 € L-1) that solved the oil models contained 81% rapeseed and 19% sunflower oils. About 10– 15 g of this mixture, alone or with olive, soya bean, wheat germ or walnut oils, also solved the meal models. Mixtures that contained a high proportion (‡50%) of the tasty olive and walnut oils also solved the models but were more expensive (4.9 € L-1 and 8.5 € L-1, respectively). Conclusions: The consumption of a mixture composed of rapeseed and sunflower oils in a 4 : 1 proportion is an inexpensive and simple way to meet current dietary recommendations for essential fatty acids and vitamin E, favouring overall dietary nutrient adequacy