In the Delboeuf illusion, a circle judged initially has a weaker effect of size induction than a circle judged subsequently (the judgment-order effect). This effect has been attributed to differential allocation of visual attention (Hamada et al, 2002 Japanese Journal of Psychology 73 58-63, in Japanese). To establish the influence of attention, in experiment I we examined whether the effect occurred mandatorily once the outer circle was attended to, or whether it was necessary to direct attention specifically to the size of the area of the outer circle. Observers trisected the circumference of the outer circle thus attending to the outer circle in terms of its circumference, but ignoring its area. The illusion was stronger when the inner-circle area estimation was followed by the outer-circle area estimation than when the inner-circle area estimation was followed by the trisection task. In experiment 2 this result was replicated by using diameter judgment, instead of the size of the area. These findings indicate that mere allocation of attention to the outer circle contour is not sufficient to produce the judgment-order effect. Rather, attention must be specific to the task-relevant dimension, in this instance the visual area, to be effective.