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This paper presents three effective proposals for a two-stage algorithm for one-microphone reverberant speech enhancement. The original algorithm is divided into two blocks: one that deals with the coloration effect, due to the early reflections, and the other for reducing the long-term reverberation. The proposed modifications consider changing the linear-prediction model order, the adaptation stepsize and stop criterion for the first algorithm stage. All the modifications are evaluated by a perceptual-quality measure specific for the speech-reverberation context. Experimental results for a 200-signal database show that the proposed improvements yielded an increase of 12% in perceptual measure and a reduction of about 96% in the computation cost when compared to the original framework.