In this paper we develop a method for the sound source separation of single channel mixtures using Independent Component Analysis within a time-frequency representation of the audio signal. We apply standard Independent Component Analysis techniques to contiguous magnitude frames of the short-time Fourier transform of the mixture. Provided that the amplitude envelopes of each source are sufficiently different, it can be seen that it is possible to recover the independent short-time power spectra of each source. A simple scoring scheme based on auditory scene analysis cues is then used to overcome the source ordering problem ultimately allowing each of the independent spectra to be assigned to the correct source. A final stage of adaptive filtering is then applied which forces each of the spectra to become more independent. Each of the sources is then resynthesised using the standard inverse shorttime Fourier transform with an overlap add scheme.