Brain-Computer Interfaces (BCIs) allow a user to control a computer application by brain activity as acquired, e.g., by EEG. One of the biggest challenges in BCI research is to understand and solve the problem of "BCI Illiteracy", which is that BCI control does not work for a non-negligible portion of users (estimated 15 to 30%). Here, we investigate the illiteracy problem in BCI systems which are based on the modulation of sensorimotor rhythms. In this paper, a sophisticated adaptation scheme is presented which guides the user from an initial subject-independent classifier that operates on simple features to a subject-optimized state-of-the-art classifier within one session while the user interacts the whole time with the same feedback application. While initial runs use supervised adaptation methods for robust co-adaptive learning of user and machine, final runs use unsupervised adaptation and therefore provide an unbiased measure of BCI performance. Using this approach, which does not involve any offline calibration measurement, good performance was obtained by good BCI participants (also one novice) after 3-6 min of adaptation. More importantly, the use of machine learning techniques allowed users who were unable to achieve successful feedback before to gain significant control over the BCI system. In particular, one participant had no peak of the sensory motor idle rhythm in the beginning of the experiment, but could develop such peak during the course of the session (and use voluntary modulation of its amplitude to control the feedback application).