We have developed a speech enhancement algorithm that is based on modified phase opponency (MPO) and a periodicity measure (Deshmukh et al. 2007) and does not need any estimate or statistical characterization of the noise. The performance of the proposed enhancement scheme, evaluated using different objective measures, is comparable to that of some of the other speech enhancement schemes when the characteristics of the background noise are not fluctuating. However, the proposed MPO-APP enhancement scheme outperforms other speech enhancement schemes when the speech signals are corrupted by fluctuating noise. Finally, unlike other enhancement schemes, the MPO-APP enhanced speech does not contain any musical noise and it is not reverberant.