76 pairs of 9- to 11-yr.-old twins (41 female, 35 male) who were discordant on the magnitude of error for the double trapezium illusion were given the Children's Personality Questionnaire and the Wechsler Intelligence Scale for Children (WISC). The Wilcoxon matched-pair signed-ranks test was used to determine whether the twins with relatively smaller magnitudes of error than their co-twins also manifested systematic differences on the personality factor scores and the WISC subtest scores. Among the female pairs, twins with smaller magnitudes of the illusion were relatively more stable (Factor C), more shrewd (Factor N), obtained higher scores on Similarities and Digit Span, and had longer reaction times before responding to the figures. Among the male pairs, similar trends were found but the differences were not as pronounced. The results are discussed in terms of Piaget's theory concerning children's deployment of attention and Kagan's reflective-impulsive dimension in children's cognitive judgments.