This work discusses the improvements which can be expected when applying linear feature-space transformations based on Linear Discriminant Analysis (LDA) within automatic speech-recognition (ASR). It is shown that different factors influence the effectiveness of LDA-transformations. Most importantly, increasing the number of LDA-classes by using time-aligned states of Hidden-Markov-Models instead of phonemes is necessary to obtain improvements predictably. An extension of LDA is presented, which utilises the elementary Gaussian components of the mixture probability-density functions of the Hidden-Markov-Models' states to define actual Gaussian LDA-classes. Experimental results on the TIMIT and WSJCAM0 recognition task are given, where relative improvements of the error-rate of 3.2% and 3.9%, respectively, were obtained.