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This paper presents a technique for Informed Source Separation (ISS) of a single channel mixture, based on the Multiple Input Spectrogram Inversion (MISI) phase estimation method. The reconstruction of the source signals is iterative, alternating between a time-frequency consistency enforcement and a re-mixing constraint. A dual resolution technique is also proposed, for sharper transients reconstruction. The two algorithms are compared to a state-of-the-art Wiener-based ISS technique, on a database of fourteen monophonic mixtures, with standard source separation objective measures. Experimental results show that the proposed algorithms outperform both this reference technique and the oracle Wiener filter by up to 3 dB in distortion, at the cost of a significantly heavier computation.