The inclusion of high specific surface materials such as calcined clays in cementitious systems enhances the hydration of clinker products at very early ages, but it may also increase water demand; thus, the pursuit of a flowing concrete may demand an increase in the dosage of superplasticizers. The grinding regime can have a major influence on the properties of the cementitious system and could help mitigate the problem of water demand. This paper discusses the impact of grinding alternatives for the production of a binder consisting of clinker, calcined clay, limestone and gypsum. Two main target products will be discussed: (i) LC3, a binder with a formulation of 50% clinker, 30% calcined clay, 15% limestone and 5% gypsum, co-ground all together, and (ii) LC2, a mineral addition with a formulation of 60% calcined clay, 35% limestone and 5% gypsum, ground separately and further blended with Portland cement on a 1:1 basis (mass). The experimental program is carried out in several stages: (i) the binder, (ii) cement pastes and (iii) standard mortars, and concrete grinding aids from the family TEA are used to enhance grinding, and their impact is also be assessed.