Higher Education plays a principal role in the changing and complex world of today, and there has been rapid growth in the scientific literature dedicated to predicting students' academic success or risk of dropout thanks to advances in Data Mining techniques. Degrees such as Computer Science in particular are in ever greater demand. Although the number of students has increased, the number graduating is still not enough to provide society with as many as it requires. This study contributes to reversing this situation by introducing an approach that not only predicts the dropout risk or students' performance but takes action to help both students and educational institutions. The focus is on maximizing graduation rates by constructing a Recommender System to assist students with their selection of subjects. In particular, the challenge is addressed of constructing reliable Recommender Systems on the basis of data which are both sparse and few in quantity, imbalanced, and anonymized, and which might have been stored under imperfect conditions. This approach is successfully applied to create a Recommender System using a realworld dataset from a public Spanish university containing performance data of a Computer Science degree course, demonstrating its successful application in real environments. The construction of a support system based on that approach is described, its results are evaluated, and its implications for students' academic achievement, and for institutions' graduation rates are discussed. Through the construction of this decision support system for students, we intend to increase the graduation rates and lower the dropout rate.