The study focuses on the problems of dimensionality reduction by means of principal component analysis (PCA) in the context of single-trial EEG data classification (i.e. discriminating between imagined left- and right-hand movement). The principal components with the highest variance, however, do not necessarily carry the greatest information to enable a discrimination between classes. An EEG data set is presented where principal components with high variance cannot be used for discrimination. In addition, a method based on linear discriminant analysis (LDA), is introduced that detects principal components which can be used for discrimination, leading to data sets of reduced dimensionality but similar classification accuracy.