Additive noise generates important losses in automatic speech recognition systems. In this paper, we show that one of the causes contributing to these losses is the fact that conventional recognisers take into consideration feature values that are outliers. The method that we call bounded-distance HMM is a suitable method to avoid that outliers contribute to the recogniser decision. However, this method just deals with outliers, leaving the remaining features unaltered. In contrast, spectral subtraction is able to correct all the features at the expense of introducing some artifacts that, as shown in the paper, cause a larger number of outliers. As a result, we find that bounded-distance HMM and spectral subtraction complement each other well. A comprehensive experimental evaluation was conducted, considering several well-known ASR tasks (of different complexities) and numerous noise types and SNRs. The achieved results show that the suggested combination generally outperforms both the bounded-distance HMM and spectral subtraction individually. Furthermore, the obtained improvements, especially for low and medium SNRs, are larger than the sum of the improvements individually obtained by bounded-distance HMM and spectral subtraction.