The accurate estimation of students' grades in future courses is important as it can inform the selection of next term's courses and create personalized degree pathways to facilitate successful and timely graduation. This paper presents future-course grade predictions methods based on sparse linear models and low-rank matrix factorizations that are specific to each course or student-course tuple. These methods identify the predictive subsets of prior courses on a course-by-course basis and better address problems associated with the not-missing-at-random nature of the student-course historical grade data. The methods were evaluated on a dataset obtained from the University of Minnesota. This evaluation showed that the course-specific models outperformed various competing schemes with the best performing scheme achieving an RMSE across the different courses of 0.632 vs 0.661 for the best competing method.