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The extensive body of economic and psychological research correlating between students' cheating and their academic grade point average (GPA) consistently finds a significant negative relationship between cheating and the GPA. However, this literature is entirely based on students' responses to direct-question surveys that inquire whether they have ever cheated on their academic assignments. The present paper examines this relationship on the basis of experimental data. It reports the results of a two-round experiment designed to expose student cheating at the individual level and correlate it with three intellectual achievement measures: the GPA, the high-school matriculation average grade (MAG) and the psychometric exam score (PES). The experiment involved two classes of third-year economics students incentivized by a competitive reward to answer a multiple-choice trivia quiz without consulting their electronic devices. While this forbiddance was deliberately overlooked in the first round, providing an opportunity to cheat, it was strictly enforced in the second, conducted two months later in the same classes with the same quiz. A comparison of subjects' performance in the two rounds, self-revealed a considerable extent of cheating in the first one. Regressing the individual cheating levels on subjects' gender and their intellectual achievement measures exhibited no significant differences in cheating between males and females. However, cheating of both genders was found to significantly increase with each achievement measure, implying, in sharp contrast with the direct-question surveys, that higher achievers are bigger cheaters.