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In this paper, we investigate the benefits of using an adaptive segmentation of the speech signal in speech enhancement. The adaptive segmentation scheme divides the signal into the longest segments within which stationarity is preserved, thus providing a good time-frequency resolution. The segmentation is performed with the help of an orthogonal library of local cosine bases using a computationally efficient tree-structured best-basis search. We show that such an adaptive segmentation results in improved speech enhancement compared to a fixed segmentation. The resulting enhanced speech is free from musical noise, without any additional smoothing.