Cement consumption in concrete can be reduced by simply mixing the right amounts of aggregates of different sizes, which result in minimum voidage. With three or more sizes of aggregates, determining their right amounts is not a trivial problem. The optimisation problem can be solved quickly after a mathematical model describing the voidage in terms of the fractions of the different sizes becomes available. When each aggregate fraction is not of a constant diameter, and the shape of the particles is not spherical, there are no simple solutions. This article describes how it is feasible to determine the optimal amounts of aggregates of three sizes using nonlinear modelling on data from a short series of well planned experiments. This approach does not require the assumptions of spherical particles or constant diameters with no variation in each size. This procedure can help save typically several percent of cement. Its environmental impact is also significant in terms of reduced carbon dioxide emissions.