We consider the local Gaussian modeling framework for under-determined convolutive audio source separation, where the spatial image of each source is modeled as a zero-mean Gaussian variable with full-rank time- and frequency- dependent covariance. We investigate two methods to improve the accuracy of parameter estimation, based on the use of local observed covariance and auditory-motivated time-frequency representation. We derive an iterative expectation-maximization (EM) algorithm with a suitable initialization scheme. Experimental results over stereo synthetic reverberant mixtures of speech show the effectiveness of the proposed methods.