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We propose a new family of Bayesian estimators for speech enhancement where the cost function includes both a power law and a weighting factor. The parameters of the cost function, and therefore of the corresponding estimator gain, are chosen based on characteristics of the human auditory system, namely, the compressive nonlinearities of the cochlea, the perceived loudness and the ear's masking properties. It is found that choosing the parameters in this way results in a decrease of the estimator gain at high frequencies. This frequency dependence of the gain improves the noise reduction while limiting the speech distortion. Experimental results show that the new estimators achieve better enhancement performance than existing Bayesian estimators such as those based on the minimum mean-square error (MMSE) of the short-time spectral amplitude (STSA), the MMSE of the logarithm of the STSA (LSA) or the weighted euclidien (WE) error, both in terms of objective and subjective measures.