Universities gather large volumes of data with reference to their students in electronic form. The advances in the data mining field make it possible to mine these educational data and find information that allow for innovative ways of supporting both teachers and students. This paper presents a case study on predicting performance of students at the end of a university degree at an early stage of the degree program, in order to help universities not only to focus more on bright students but also to initially identify students with low academic achievement and find ways to support them. The data of four academic cohorts comprising 347 undergraduate students have been mined with different classifiers. The results show that it is possible to predict the graduation performance in 4th year at university using only pre-university marks and marks of 1st and 2nd year courses, no socio-economic or demographic features, with a reasonable accuracy. Furthermore courses that are indicators of particularly good or poor performance have been identified.