We extend the existing literature on food taxes targeting obesity. We systematically incorporate the implicit substitution between added sugars and solid fats into a comprehensive food demand system and evaluate the effect of taxes on sugars and fats. The approach conditions how food and obesity taxes affect total calorie intake. The proposed methodology accounts for the ability of consumers to substitute leaner low-fat and low-sugar items for rich food items within the same food group. This substitution is integrated into a calibrated demand system in addition to the substitution among food groups, using recent food intake data and existing demand elasticities. Simulations of taxes on added sugars and solid fat show that their impact on consumption patterns is understated and the induced welfare loss is overstated when abstracting from the substitution possibilities within food groups.