Exams play a key role in a student's learning process at university, and their organization may affect student performance. A high number of retakes, for instance, could encourage procrastination or reduce effort for each attempt. This article investigates the effects of a policy change at a major Italian university that reduced the number of exam retakes allowed per subject from six to three. Using a difference-in-differences strategy, we find that this policy significantly improved first-year outcomes, including lower dropout rates, higher exam pass rates, and increased credit accumulation. We conduct several robustness checks showing that only a small fraction of these improvements can be attributed to changes in the average quality of students enrolled following the reform. Additionally, the policy contributed to an increase in on-time graduation rates, which was the main objective of the reform, without harming student GPA. This study shows that implementing a cost-effective policy, such as limiting exam retakes, can substantially enhance student progression, reducing age at graduation.