The new model reduces the impact of local spectral and temporal variability by estimating a finite set of spectral and temporal warping factors which are applied to speech at the frame level. Optimum warping factors are obtained while decoding in a locally constrained search. The model involves augmenting the states of a standard hidden Markov model (HMM), providing an additional degree of freedom. It is argued in this paper that this represents an efficient and effective method for compensating local variability in speech which may have potential application to a broader array of speech transformations. The technique is presented in the context of existing methods for frequency warpingbased speaker normalization for ASR. The new model is evaluated in clean and noisy task domains using subsets of the Aurora 2, the Spanish Speech-Dat-Car, and the TIDIGITS corpora. In addition, some experiments are performed on a Spanish language corpus collected from a population of speakers with a rang...