In this paper, we present a new speech enhancement method that processes noise-corrupted speech in the discrete cosine transform (DCT) modulation domain. In contrast to the Fourier transform, the DCT produces a real-valued signal. Therefore, modulation-based processing in the DCT domain may allow both acoustic Fourier magnitude and phase information to be jointly estimated. Based on segmental SNR and the results of blind subjective listening tests on speech corrupted with various coloured noises, the application of the subspace method in the DCT modulation domain processing was found to outperform all other methods evaluated, including the LogMMSE method.