In this paper, a generalised Villeneuve type linear array distribution is developed, which permits the direct synthesis of discrete array distributions for high efficiency sum patterns of arbitrary sidelobe level and envelope taper. With the Dolph–Chebyshev distribution as the parent space factor, and the correct perturbation of these space factor zeros, the excitation efficiency and beamwidths are kept as close to their optimum values as is possible under the given sidelobe ratio and envelope taper conditions. The method is the discrete analogue of the generalised Taylor n̅-distribution, used for continuous line source synthesis. Examples are given to illustrate the principal features of the distribution.