This work presents a method for designing the weighting parameter required by Wiener-based binaural noise reduction methods. This parameter establishes the desired tradeoff between noise reduction and binaural cue preservation in hearing aid applications. The proposed strategy was specially derived for the preservation of interaural level difference, interaural time difference and interaural coherence binaural cues. It is defined as a function of the average input noise power at the microphones, providing robustness against the influence of joint changes in noise and speech power (Lombard effect), as well as to signal to noise ratio (SNR) variations. A theoretical framework, based on the mathematical definition of the homogeneity degree, is presented and applied to a generic augmented Wiener-based cost function. The theoretical insights obtained are supported bycomputational simulations and psychoacoustic experiments using the multichannel Wiener filter with interaural transfer function preservation technique (MWF-ITF), as a case study. Statistical analysis indicates that the proposed dynamic structure for the weighting parameter and the design method of its fixed part provide significant robustness against changes in the original binaural cues of both speech and residual noise, at the cost of a small decrease in the noise reduction performance, as compared to the use of a purely fixed weighting parameter.