The first class based adaptation approaches [FGH + 97, Ueb97] take the use of classes in the construction of statistical m-gram models one significant step further than just using them as a smoothing technique: The m-gram of classes is trained on the large background corpus while the word likelihoods given the class are estimated on the small target corpus. To make full use of this technique a specialized clusteralgorithm has been developed [FGH + 97, Ueb97]. In this paper we extend class adaptation to make use of the m-gram distribution of the target domain. As a second independent contribution this paper introduces an efficient morphing algorithm, that tries to achieve adaptation by using a stochastic mapping of words between the vocabularies of the respective domains. As a result we can show, that for small adaptation steps class based adaptation is a very useful technique. For larger adaptation steps the perplexity of the modified model is greatly improved, yet no improvement over the unadapted model was observed when used in linear interpolation. Whether this is due to the fact that we use class based adaptation or that we do just modify the unigram distribution is still unresolved, although the new stochastic mapping technique might help to give an answer to this question in the future.