This study surveyed underachieving gifted students and their parents in order to: determine the extent and sources of positive and negative attitudes toward educational acceleration, compare the views of parents and students for congruence, and compare the perceptions of successful students and their parents with the views of identified underachieving students and their parents. Data from 15 students and their parents indicated few concerns that acceleration would have negative effects on leadership, academic achievement, or creativity. The overriding concern of parents and students was for the potentially negative effects that acceleration would have on social and emotional development. Eight of the parents indicated that they had considered acceleration for their children, seven of these decided to accelerate their children, and all but one of the seven stated that the decision to accelerate worked out well. Parents and students from the underachieving sample held generally similar perceptions of potential harm compared to a sample of successful students and their parents. (Includes 11 references) (JDD)