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This work addresses the mitigation of channel errors by means of efficient minimum mean-square-error (MMSE) estimation. Although powerful model-based implementations have been recently proposed, the computational burden involved can make them impractical. We propose two new approaches that maintain a good level of performance with a low computational complexity. These approaches keep the simple structure and complexity of a raw MMSE estimation, although they enhance it with additional source a priori knowledge. The proposed techniques are built on a distributed speech recognition system. Different degrees of tradeoff between recognition performance and computational complexity are obtained.