Purportedly fear of the unknown, death anxiety, and insomnia are prevalent problems among some gifted individuals. The present study tested this assertion and examined the relationship of these variables to Dabrowski's (1967) overexcitabilities. The study involved 73 gifted and 143 typical middle and high school adolescents who were given a death anxiety questionnaire, a fear of the unknown scale, an insomnia scale, and the Overexcitabilities Questionnaire II (R. F. Falk, S. Lind, N. B. Miller, M. M. Piechowski & L. K. Silverman, 1999). Gifted adolescents reported higher levels of fear of the unknown and insomnia than regular students. They also scored higher on three of Dabrowski's overexcitabilities. Higher levels of overexcitability in gifted students were associated with higher anxiety and insomnia. The results suggest that some gifted students who are experiencing overexcitabilities, insomnia, fear of the unknown, and/or death anxiety may benefit from curriculum aimed at social and emotional development, bibliotherapy, fantasy gaming, relaxation techniques, and counseling.