In this paper we present an improved version of the recently proposed Maximum A-Posteriori (MAP) based noise power spectral density estimator. An empirical bias compensation and bandwidth adjustment reduce bias and variance of the noise variance estimates. The main advantage of the MAP-based postprocessor is its low estimation variance. The estimator is employed in the second stage of a two-stage single-channel speech enhancement system, where eight different state-of-the-art noise tracking algorithms were tested in the first stage. While the postprocessor hardly affects the results in stationary noise scenarios, it becomes the more effective the more nonstationary the noise is. The proposed postprocessor was able to improve all systems in babble noise w.r.t. the perceptual evaluation of speech quality performance.