In this study, two solution approaches are compared for a real-world, moderate-size but a highly constrained university course timetabling problem. The first approach is developing an integer programming model and solving it by using a mixed integer programming solver while the second approach is developing a constraint programming model for the same problem and solving it by a constraint programming optimizer. A performance comparison of the two methods in terms of solution quality and computational time is presented. Different constraint configurations of the problem have been created, and the two solution methods have been compared under these constraint configurations. For most of the configurations, it has been observed that the performances of the two methods do not significantly differ in terms of solution quality provided that there are enough system resources for each model. Available system resources also happen to be among the factors that affect the performance.