Musical residual noise is a major problem for a speech enhancement system. This noise is very annoying to the human ear and can significantly deteriorate the perception quality of enhanced speech. In this study, we aim at reducing the quantity of musical residual noise by a two-stage speech enhancement approach. In the first stage a preprocessor enhances noisy speech using an algorithm which combines the two-step-decision-directed and the Virag methods. In the second stage the enhanced speech signal is post-processed by an iterative-directional-median filter to significantly reduce the quantity of residual noise, while maintaining the harmonic spectra. Experimental results show that the proposed approach can significantly improve the performance of a speech enhancement system by reducing the quantity of residual noise.