In order to make speech recognition technology viable in realistic environments, high performance in noise has become an important goal for speech recognition research. We present a Hidden Markov Model (HMM) cepstral noise compensation method which effectively uses the available information about the speech signal and the background noise, thereby improving recognition performance significantly with only a minimal computational load. The algorithm is based on Wiener filtering the corrupted signal, which corresponds to a multiplication in the frequency domain of the noisy speech spectrum and the Wiener filter frequency response. In the quefrency domain this corresponds to an addition. Therefore if the frequency response of the Wiener filter can be estimated, the cepstral representation of this filter can be applied as an additive correction factor during recognition. Comparative testing shows that cepstral compensation performs as well or better than other current noise-robust methods, usually at a much lower computational cost.