This paper describes a method of enhancing speech corrupted by additive uncorrelated noise. The approach adopted is to use cepstral-domain hidden Markov models to determine statistics of the clean speech and noise processes. A compensated model of speech corrupted by noise is generated using parallel model combination. MMSE and linear non-homogeneous estimators of the clean speech signal are derived. The enhancement system gives natural-sounding speech without the artifacts introduced by systems such as spectral subtraction. HMM recognition tests performed on the enhanced speech using the NOISEX-92 database show a significant reduction in error rate.