Many beam-forming algorithms available for hearing aids, preserve both the interaural time differences (ITDs) and the interaural level differences (ILDs) of the interferers. Constraining both the spatial cues over all frequencies will exhaust the degrees of freedom (DoF) available for noise reduction in the filter design. The binaural cues, however, are frequency selective, i.e., the ITDs are dominant in the frequency range below 1.5 kHz and the ILDs are dominant at frequencies above 1.5 kHz. Hence in this paper, we propose two methods to preserve only the ILDs of the interferers, in the higher frequencies, while keeping the target undistorted. Since these formulations are nonconvex, quadratically constrained quadratic programs (QCQPs), an approximate convex relaxation is proposed. The proposed methods preserve the ILDs in the higher frequencies while an available algorithm that preserves interaural transfer function (ITF) of the interferers is used for the lower frequencies. The performance of the methods proposed are evaluated through simulations and the localization performance is validated through informal listening tests.@en