A modified Voronoi tessellation (MVT) is proposed for the computer simulation of realistic microstructures. Compared with standard tessellations, the present algorithm provides the desired grain size distribution in a one-step, non-evolutionary procedure. This is obtained by relaxing the constraints of Voronoi tessellation on position and orientation of the grain boundaries, with the only side effect being the formation of a limited amount of eliminable voids. As an example, it is shown how to directly obtain a distribution of grains of given variance and with a shape statistically close to the lognormal one.