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In this paper, we propose a novel and simple approach for dealing with the exaggerated extrinsic information produced by the soft-output Viterbi algorithm (SOVA). The proposed remedy is based on mathematical analysis and it involves using two attenuators, one applied to the immediate output of the SOVA and another applied to the extrinsic information before it is passed to the other decoder (assuming iterative decoding). The use of these attenuators aims at reducing the inherent strong correlation between the intrinsic information (input to the SOVA) and extrinsic information (output of the SOVA). We examine the modified SOVA (MSOVA) on additive white Gaussian noise (AWGN) and flat fading channels for parallel concatenated codes (PCCs) and serial concatenated codes (SCCs). We show that the MSOVA provides substantial performance improvements over both channels. For example, it provides improvements of about 0.8 to 1.0 dB at Pb = 10-5 in AWGN, and about 1.4 to 2.0 dB at Pb = 10-5 on fading channels. We also show that there are cases where the MSOVA is superior to the a posteriori probability (APP) algorithm. With this motivation, we extend the proposed modification to the APP algorithm with favorable results. We demonstrate that the modified APP (MAPP) provides performance improvements between 0.3 to 0.6 dB at Pb = 10-5 relative to the APP. We lastly mention that the proposed modifications, while they provide considerable performance improvements, keep the complexity of these decoders almost the same, which is remarkable.