Healthier dietary patterns involve more plant-based foods than current Western diets rich in animal products containing high levels of bioavailable iron and zinc. Little consideration is given to the bioavailability of iron and zinc when studying healthy eating patterns. Our aim was to determine whether currently estimated requirements for bioavailable iron and zinc limit the identification of healthier dietary patterns. Using dietary data from a representative French survey and multi-criteria non-linear optimization, we identified diets that maximize health criteria based on Food-Based Dietary Guidelines and concomitantly depart only minimally from the observed diet, while complying with all nutrient reference values either strictly (non-flexible optimization) or by allowing bioavailable iron and zinc below the current reference values, but to a limited extent (flexible optimization). Using a comparative risk assessment model, we estimated the resulting impact on cardiometabolic and colorectal cancer mortality/morbidity, and changes to iron-deficiency anemia. Under non-flexible optimization, reference values for bioavailable iron and zinc were the most binding of the 35 nutrient constraints and modeled diets displayed considerable redistributions within grains and meat. With flexible optimization, modeled diets were healthier as they contained less red meat and more whole-grain products, but would increase iron-deficiency anemia to 5.0% (95% CI: 3.9%, 6.4%). Globally, in terms of Disability Adjusted Life Years (DALYs), as the loss due to anemia would represent <30% of the gain otherwise made on chronic diseases, adding flexibility in the iron and zinc reference values would result in a further 18% decrease in the disease burden from 84,768 (95% Uncertainty Intervals (UI): 81,066, 88,470) to 99,689 (95,787, 103,591) DALYs averted. Currently estimated requirements for bioavailable iron and zinc proved to be critical factors when modelling healthy eating patterns. Considering lower reference values enables the identification of diets that are apparently healthier overall.