This paper presents the improvements that can be achieved through the additional constraints in the design of highly sparse arrays beamforming. The design of a highly sparse array beamformer is an optimization problem of multivariable functions and its performance depends on the given conditions. For a uniform linear array (ULA), the Output Signal to Noise Ratio (OSINR) is a linear function of antenna elements of the array. However, this linearity is not consistent in various antenna array environments. This deviation can be minimized by selecting an optimal sparse array with a lesser number of elements than that are actually required by an ULA. In this paper, a two-step procedure has been presented to find an optimal solution for designing a highly sparse antenna array beamformer with sidelobe control. Furthermore, to avoid the grating lobes and minimize the mutual coupling between the elements an additional degree of freedom in the form of separation between antenna elements is added to the optimization problem. Simulations results provided in the paper reveals that sparse arrays with the additional conditions are better in comparison with the arrays without constraints in terms of sidelobe level, grating lobes and mutual coupling.