People tend to rate exceptional levels of IQ (99th percentile) as less attractive than high levels of IQ (90th percentile), and it remains to be determined why. Furthermore, the desirability of emotional intelligence (EI) in a prospective partner has yet to be investigated. Finally, we sought to determine whether individual differences in self-assessed and objectively measured IQ/EI correlated with desirability ratings of IQ/EI in a prospective partner. Based on a general community sample (N = 236) and an undergraduate sample (N = 220), we found that the association between rated desirability and the IQ/EI level of a prospective partner exhibited a threshold effect at the 90th IQ/EI percentile. Furthermore, a statistically significant decrease in rated desirability between the 90th to the 99th percentiles was observed for IQ, but not for EI. We found that participants who reduced their ratings of desirability between the 90th and 99th IQ percentiles did so due to compatibility concerns (≈60%) and social skill concerns (≈40%). We also found that self-assessed IQ and objectively measured IQ correlated positively with desirability ratings at the 90th IQ percentile, and self-assessed EI (but not objectively measured EI) with desirability ratings at the 90th EI percentile. Finally, we found that, on average, people ranked/rated EI to be somewhat more desirable than IQ. We interpreted the results as consistent with compatibility theory, active assortative mating for intelligence, and the possibility that many people subscribe to the stereotype that exceptionally intelligent people suffer from interpersonal skill difficulties.