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Within the last three decades research in single-channel speech enhancement has been mainly focused on filtering the noisy spectral amplitude without that much focus on the integration of phase-based signal processing. Recently, several phase-aware algorithms based on phase-sensitive signal models were proposed for speech enhancement using the minimum mean squared error (MMSE). Improved performance over the conventional phase-insensitive approaches has been achieved. In this paper, we propose an iterative joint maximum a posteriori (MAP) amplitude and phase estimator (ijMAP) assuming a non-uniform phase distribution. Experimental results demonstrate the effectiveness of the proposed method in recovering both amplitude and phase in noise, justified by perceived quality, speech intelligibility and phase estimation error instrumental measures. The proposed method, brings joint improvement in perceived quality and speech intelligibility compared to the phase-blind joint MAP estimator with a comparable performance to the complex MMSE estimator.