To what degree does our representation of the immediate world depend solely on its relevance to what we are currently doing? We examined whether relevance per se can cause "blindness," even when there is no resource limitation. In a novel paradigm, people looked at a colored circle surrounded by a differently colored ring--the task relevance of which was previously manipulated--and were subsequently asked to identify these colors. Whereas knowledge of the task-relevant color was near perfect, up to a quarter of the participants could not name the color of the irrelevant stimulus, even though a control experiment indicated there were sufficient resources to process both stimuli. The results are a first demonstration of blindness when mental resources are clearly available and challenge attentional theories predicting strong selection only when resources are taxed. (Contains 2 figures and 6 footnotes.)