For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the corresponding complex-valued STFT. Most authors in this field choose a Wiener-like filtering approach which boils down to using the phase of the original mixture. In this paper, a different standpoint is adopted. Many music events are partially composed of slowly varying sinusoids and the STFT phase increment over time of those frequency components takes a specific form. This allows phase recovery by an unwrapping technique once a short-term frequency estimate has been obtained. Herein, a novel iterative source separation procedure is proposed which builds upon these results. It consists in minimizing the mixing error by means of the auxiliary function method. This procedure is initialized by exploiting the unwrapping technique in order to generate estimates that benefit from a temporal continuity property. Experiments conducted on realistic music pieces show that, given accurate magnitude estimates, this procedure outperforms the state-of-the-art consistent Wiener filter.