As speech technology is applied to real world applications there is a need to build systems that are insensitive to differences in training and test conditions. These differences may result from ambient background noise, channel variations, speaker stress etc. A variety of techniques have been applied to this problem. This paper examines one class of approach, model-based compensation. In particular, where a speech model is combined with an "additive noise" model, "channel" model and, in the general case, a speaker stress model, to generate a corrupted-speech model. Various schemes for performing this compensation will be described along with the advantages and, of course, the disadvantages of such an approach. In addition, methods for combining the approach with compensation schemes which make use of speech data in the new environment will be detailed. This combined approach overcomes some of the limitations of the standard "nice" schemes.