The paper first examines the issue of the beampattern dependency on the choice of phase centre location, when a narrow band beamformer is subjected to directional and spatial derivative constraints. It is shown that the norm of the weight vectors for a zero-plus-first and zero-plus-first-plus-second derivative constrained beam-formers, under white noise conditions, is a quadratic and a quartic function of a parameter which specifies the phase centre location. The paper then presents a technique based on a power response approach, for deriving a new set of constraints for controlling the beampattern spatial derivates. The new set of constraints ensure that the array beam-pattern is independent of the choice of the phase centre co-ordinate origin. It is shown that for the first-order case, the constraint is linear, but for the second-order case, the constraint is quadratic. The paper then presents a technique for approximating the effect of the quadratic constraint by two linear constraints. It is shown that by using these two sets of linear constraints, the dependency of the beampattern on the choice of the phase centre co-ordinate origin cannot be totally eliminated, but the effect has been very much reduced. Finally, the paper presents a technique for optimising the beampattern with respect to the choice of the phase centre location, when the quadratic constraint is being approximated with linear con-straints. Numerical results showed that the optimised version has a better performance in terms of maintaining beamwidth broadening and capability of rejecting interferences.