This paper describes the optimisation of small arrays of Wave Energy Converters (WECs) of point absorber type. The WECs are spherical in shape and operate in heave alone and a linear array of five devices is considered. Previous work is extended by considering the constrained performance of the array members, where an uaniper limit on WEC displacements is enforced. Two opimisations are performed. In each case, the objective function is defined as the mean of the averaged interaction factor ovehe non-dimensional length of the array. The first considers the array layout fixed at a geometry previously identified as optimal in an unconstrained regime and optimises the displacements of the WECs subject to constraints. The second allows both the WEC positions and displacements to vary as optimisation variables. It is shown that the optimal layout of the constrained arrays is different from the unconstrained case. Applying constrained motions results in optimal layouts that are more separated, with less grouping of WECs and this will have practical considerations. The effect of the constraints varies depending on the incident wave angle. In some cases, performance is reduced drastically and stability of performance is improved, while in other cases there is a degradation of performance. Thus, a trade-off between performance and stability of performance is seen when displacement constraints are applied.