Background: When students are given a choice of when to take an exam in engineering and computing courses, it has been previously observed that average exam scores generally decline over the exam period. This trend may have implications both for the design of interventions to improve student learning and for data analysis to detect collaborative cheating. Purpose/Hypothesis: We hypothesize that average exam scores decline over the exam period primarily due to self-selection effects, where weaker students tend to choose exam times later in the exam period, while stronger students are more likely to choose earlier times. Design/Method: We collected 31,673 exam records over four semesters from six undergraduate engineering and computing courses that had both synchronous exams (all students at the same time) and asynchronous exams (students choose a time). We analyzed student exam time choice and asynchronous exam scores, using synchronous exam scores in the same course as a control variable. Results: We find that students with lower scores on synchronous exams generally elect to take asynchronous exams later and that controlling for student ability (via synchronous exams) removes 70% of the decline observed in average asynchronous exam scores over the exam period but does not eliminate the downward trend with time. Conclusions: We conclude that self-selection effects are primarily responsible for exam score declines over time, that exam time selection is unlikely to be a useful target for interventions to improve performance, and that there is no evidence for widespread collaborative cheating in the dataset used in this research.